Question

In: Statistics and Probability

1. In the following problem, check that it is appropriate to use the normal approximation to...

1. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities
It is estimated that 3.4% of the general population will live past their 90th birthday. In a graduating class of 750 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday

(b) 30 or more will live beyond their 90th birthday

(c) between 25 and 35 will live beyond their 90th birthday

(d) more than 40 will live beyond their 90th birthday

2. Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45.4 months and a standard deviation of 7.7 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)


(b) If Quick Start does not want to make refunds for more than 13% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

Solutions

Expert Solution

(a)

The probability that 15 or more will live beyond their 90th birthday, using continuity correction factor,  is equal to

(b)

The probability that 30 or more will live beyond their 90th birthday, using continuity correction factor,  is equal to

(c)

The probability that between 25 and 35 will live beyond their 90th birthday, using continuity correction factor,  is equal to

(d)

The probability that 40 more will live beyond their 90th birthday, using continuity correction factor,  is equal to

orchestra answered 1 year ago
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