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# Standard deviation and probability

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A tire manufacturer believes the tread life of its snow tires can be described by a normal distribution with a mean of 32,000 miles and a standard deviation of 7000 miles. Find the probability (rounding to tenth of percent) that a randomly selected tire will have a tread life: a. of at least 40,000 milesb. of 30,000 or less milesc. that last between 30,000 and 35,000 miles (include the boundaries)d. In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer doesn’t want to take too big a financial risk with this guarantee. If the dealer is willing to give refunds to no more than 1 out of every 50 tires sold, for (Round to the nearest whole number)e. Find the probability that 50 randomly chosen tires will have a mean tread wear of greater than 35,000 miles ? (Round to tenth of a percent

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