Suppose that the average annual cost of automobile insurance is $850 with an estimated population standard deviation of $245
a.)What is the probability that a simple random sample of size 150 insured automobiles will have a sample mean insurance cost greater than $950?
b.)What is the probability that a simple random sample of size 50 insured automobile will have a sample mean insurance cost within $25 of the population mean?
a)
for normal distribution z score =(X-μ)/σ | |
here mean= μ= | 850 |
std deviation =σ= | 245.0000 |
sample size =n= | 150 |
std error=σx̅=σ/√n= | 20.0042 |
probability = | P(X>950) | = | P(Z>5)= | 1-P(Z<5)= | 1-1= | 0.0000 |
b)
probability = | P(825<X<875) | = | P(-0.72<Z<0.72)= | 0.7642-0.2358= | 0.5284 |
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