POSNER, Circuit Judge.

This appeal in a diversity case governed by the common law of Wisconsin requires us to consider an interesting problem in the law of insurance contracts. On June 25, 1982, Lane Smith, a successful businessman who was 41 years old, signed an application for a $100,000 life insurance policy to be issued by the North American Company for Life and Health Insurance, and executed a form indicating that he was not a smoker. He gave the insurance agent (an independent agent named Jacobson) a check for $141, representing the first year's premium due under the policy, and received in exchange a conditional receipt which stated that the insurance would be in effect from the date of the application, provided that Smith "on this date [was] acceptable to the Company under its rules and practices as standard risks on the plan and for the amount applied for." In the space provided on the form for "plan," Jacobson wrote "ART." North American has no plan called "ART"; the acronym refers not to a specific plan but to a class of plans known as "annual renewable term" life insurance. En route to North American, intermediate insurance agencies altered Smith's application to substitute "Graduate" for "ART" and then "Graduate Preferred" for "Graduate." "Graduate Preferred" is the name of a North American annual renewable term life insurance plan which costs $141 a year (what Smith paid Jacobson) for a man of Smith's age and requires that the insured not be a smoker. Apparently neither Smith nor Jacobson knew the name of the policy.

The application asked whether the applicant had ever had or been treated for high blood pressure, to which Smith answered "no." He also answered "no" to the question whether he had consulted a doctor within the last five years. In processing Smith's application North American discovered that Smith had in fact received medical treatment for high blood pressure within the previous three to five years. On July 22, 1982, North American sought additional information about Smith's blood pressure, and on August 4 it asked him to submit to a medical examination and provide a urine specimen. On August 1, however, Smith had drowned in a boating accident. After discovering that Smith had consulted a doctor at least nine times in the last five years for sciatic pain and high blood pressure and had been taking medication for high blood pressure throughout this period (he had refilled his prescription last on May 13, 1982, six weeks before he applied for the life insurance), North American informed Smith's widow that it would not honor the conditional insurance contract. The district court found after a bench trial that Smith's misrepresentations had been material, and therefore entered judgment for the insurance company.

The parties agree that Smith's death during the processing of his application for life insurance did not make the contract lapse. North American was duty-bound to complete its investigation, and if the investigation had shown that Smith (if he had survived) would have been contractually entitled to the issuance of the insurance policy on which he paid the first premium, the company owes his beneficiaries $100,000. See, e.g., Brown v. Equitable Life Ins. Co., 60 Wis.2d 620, 627-28, 211 N.W.2d 431, 435 (1973). Since, however, by definition the company would not have insured Smith if he made material misrepresentations in the application, it owes the beneficiaries nothing if his misrepresentations were material. See, e.g., Gibson v. Prudential Ins. Co., 274 Wis. 277, 289-90, 80 N.W.2d 233, 240 (1956).

The problem arises from Smith's death before the insurance company completed its investigation. If the investigation had been completed and had revealed that Smith had only mildly elevated blood pressure well controlled by medication, the insurance company might have insured him anyway. But in deciding how likely this is, it becomes important just what insurance policy Smith was applying for. If as the district judge found it was the "Graduate Preferred" policy, the misrepresentations were material; the company would not have insured Smith under a plan designed for people in the very pink of health. But the application did not say "Graduate Preferred," and the conditional receipt said that the applicant would be insured if he met the requirements for "standard risks" — not the below-average risks for which the "Graduate Preferred" plan is designed. Since nothing in the application, the conditional receipt, or Jacobson's oral representations suggests that Smith was told he was applying for a policy for which he was ineligible if (as turned out to be the case) he had high blood pressure, rather than a policy with less demanding requirements that he might well have satisfied despite that condition, it seems that the company is trying to enforce a term to which Smith never agreed.

But asking whether Smith "agreed" to the underwriting standards of the "Graduate Preferred" policy is the wrong question. The right question is whether Smith applied for the "Graduate Preferred" policy or for some other policy. If the former, then he was stuck (at least in the absence of misrepresentations by the insurance company or its agents) with whatever happened to be the underwriting standards applicable to that policy. Normally a person does not know, when he applies for life insurance, what the underwriting standards are. No doubt he assumes that if he answers all the health questions "no" he will be insured, but he does not know what will happen if he answers some of them "yes." He consents to whatever the standards are, provided they are not applied in a selective fashion to him, and there is no suggestion they were here. The point is perfectly general: you might buy a bicycle and find that you could not learn to use it and hence that it was worthless to you; but that would not change the fact that you had bought it pursuant to a valid contract of sale — unless, of course, the seller had made misrepresentations to induce the sale. Often when people buy things they are gambling about what they are actually getting, and that was the case here.

Smith filled out the nonsmoker form, which pertains only to the "Graduate Preferred" policy, and he paid the exact premium due under that policy for the first year. No other policy offered by North American carries the same premium. Jacobson obviously did not pull the figure $141 out of his hat. It was the premium for the "Graduate Preferred" policy, whether he knew the name or not. Any other North American "annual renewable term" policy would have carried a substantially higher annual premium (either $221 or $329). The problem of the written contract that does not unambiguously identify the subject matter of the transaction is not a new one in contract law. See Raffles v. Wichelhaus, 2 Hurl. C. 906, 159 Eng. Rep. 375 (Ex. 1864). In such a case the court must gather the meaning of the contract (if there was a contract, a meeting of the minds) from whatever evidence is presented. See, e.g., Kraemer Bros., Inc. v. United States Fire Ins. Co., 89 Wis.2d 555, 562, 278 N.W.2d 857, 860 (1979); Frigaliment Importing Co. v. B.N.S. Int'l Sales Corp., 190 F. Supp. 116 (S.D.N.Y. 1960) (Friendly, J.). Although ambiguities in insurance policies are resolved in favor of coverage, see, e.g., Katze v. Randolph Scott Mutual Fire Ins. Co., 116 Wis.2d 206, 213, 341 N.W.2d 689, 692 (1984), we are not sure that this precept is applicable when the question is not what the policy said but which policy the insured applied for. The precept seems related to the fact that the purpose of an insurance contract is to shift risk from the insured to the insurer; and if one does not know whether an applicant for insurance wanted to be insured on the terms offered by the insurer, the precept does not seem to be particularly relevant. Anyway the district judge did not consider this a close case, the sort to which the precept applies; and there was sufficient evidence (the amount of the premium being the clincher) to support her finding that the parties were contracting with reference to the "Graduate Preferred" policy, whatever they called it. So Smith was stuck with whatever happened to be the underwriting standards for that policy, and his beneficiaries must lose.

The case might be different if Jacobson had misled Smith. Suppose Smith had leveled with Jacobson about his high blood pressure and Jacobson had responded that it made no difference — that the company would still insure him for $141. Then there would be an issue of promissory estoppel: whether Smith had relied on Jacobson's representation to his detriment and forgone an opportunity to obtain either a higher-priced policy from North American, or a competitor's policy, in the short time that remained (though of course Smith did not know that only a short time remained) to his death. Cf. Ryder v. State Farm Mutual Automobile Ins. Co., 51 Wis.2d 318, 323-25, 187 N.W.2d 176, 179-80 (1971). The fact of Jacobson's misrepresentation would not be enough, however; the plaintiffs would also have to show that Smith would have bought another policy despite its higher price. But in fact there is no evidence either that Jacobson misrepresented Smith's eligibility for the "Graduate Preferred" policy (Jacobson did not know about Smith's high blood pressure) or that Smith would have paid a higher price for a different policy. The plaintiffs' argument is not one of promissory estoppel at all; it is that Smith signed a contract for a different policy from the "Graduate Preferred" and one for which he was eligible despite his high blood pressure. The district judge found that Smith had not signed a different contract, and her determination on the point was not clearly erroneous and must be accepted.

Still another possibility is that the contract was not for a specific policy, but for any policy that Smith might be eligible for; on this interpretation the $141 that he paid Jacobson was a kind of down payment or a payment on account, and if it turned out that he was not eligible for such a cheap policy the company would bill him for the difference between the premium for a more expensive substitute and the $141 he had paid. If this was the contract then the company broke it, provided Smith was eligible for any of the annual renewable term policies that the company offered. But the district judge was not required to accept this characterization of the contract either, when there was no evidence that Smith was prepared to commit himself to pay a higher premium for another policy if his application for the "Graduate Preferred" policy was turned down.

We need not consider the district judge's alternative ground, which is that Smith's representations were material even if he actually was applying for a standard policy that did not require the applicant to have normal blood pressure. It seems conceded all around that if the medical examination that North American wanted Smith to take showed that his blood pressure was being controlled by the medication, North American would have offered to insure him — though not under the "Graduate Preferred" policy. Unless he presented evidence that he would in fact have accepted a standard policy despite the higher price, there would be no basis for arguing that that was the policy he applied for, and therefore the question whether the company would have issued him such a policy would not arise. But set that problem to one side by assuming that he would in fact have accepted the more expensive policy. Then the question whether his misrepresentations were material to the issuance of the more expensive policy would, given the absence of the direct evidence that a completed investigation would have provided, depend on who had the burden of proving materiality; and it was the insurance company. Gibson v. Prudential Ins. Co., supra, 274 Wis. at 287, 80 N.W.2d at 238. This makes us skeptical of the district judge's alternative holding, especially when the judge prefaced her finding of materiality with the statement, "I think a very strong argument can be made for the proposition that Mr. Smith would have been acceptable as a standard risk on the graduate standard plan if that is or if that had been the plan that he had applied for and for which he had paid." His blood pressure was only mildly elevated and had been brought down to normal by the mild antihypertensive drug that had been prescribed for him.

But even if Smith's misrepresentations would not have been material if he had applied for some policy other than the "Graduate Preferred" policy, the district judge's finding, which we have upheld, that that was the plan he applied for requires us to affirm the judgment for the insurance company. Smith applied for cut-rate insurance subject to whatever the underwriting standards for such insurance turned out to be, thereby assuming a risk of being found uninsurable, in exchange for the lower premium if he was found insurable. As the risk he assumed materialized, his beneficiaries are not entitled to the proceeds of the policy.

AFFIRMED.