Question

Answer questions 23 and 24 based on the following:

The mean annual cost of automobile insurance is $939. The standard deviation is $300. You have been asked to compute the probability that a simple random sample of automobile insurance policies of size 100 will have a sample mean within $30 of the population mean.

23. Compute the standard deviation of the population.

(a) $300 (b) $3 (c) $1.73 (d) $5.48 (e) $30

24. Compute the probability that a simple random sample of automobile insurance policies of size 100 will have a sample mean within $30 of the population mean.

      (a) .0638 (b) .0319 (c) .5934 (d) .2967 (e) .6826

25. Which of the following is not a characteristic of the normal distribution?

      (a) the mean, median and mode are equal (b) the mean of the distribution can be negative, zero, or positive (c) the distribution is symmetrical (d) the standard deviation must be 1

Answer 1

Given xa. Cost of Automobile insurance e-8939, or $300 na100 23) using central limit theorem Sampling distribution of sample mean is approximatly normally distributed with en u28939 Od Šo 300$30 Jou 24 p( g. 4-zoolac u +30) za boa Nr Corol z - Plu-300-14 6 = P(-30 ar 4 +30-4 ] sł ) 3 apo ILALI) = P(241) - P(24-1) = 0 - 8413 - 0.1586 - 0.6827 the following d) the standard deviation is must be. 1 is not a characteristic of normes distribution