Question

CNNBC recently reported that the mean annual cost of auto insurance is 996 dollars. Assume the standard deviation is 282 dollars, and the cost is normally distributed. You take a simple random sample of 7 auto insurance policies. Round your answers to 4 decimal places.

What is the distribution of X? X ~ N

What is the distribution of ¯x? ¯x ~ N

What is the probability that one randomly selected auto insurance is less than $954?

a simple random sample of 7 auto insurance policies, find the probability that the average cost is less than $954.

For part d), is the assumption of normal necessary? yes or no

Answer 1

Solution :

Given that ,

mean = = $996

standard deviation = = $282

a.

X N (996 , 282)

b

n = 7

= $996

= / n = 282 / 7 = 106.5860

N (996 , 106.5860)

c.

P(x < $954) = P[(x - ) / < (954 - 996) / 282]

= P(z < -0.15)

= 0.4404

Probability = 0.4404

d.

P( < $954) = P(( - ) / < (954 - 996) / 106.5860)

= P(z < -0.39)

= 0.3483

Probability = 0.3483

e.

yes