CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 234 dollars. You take a simple random sample of 61 auto insurance policies. Find the probability that a single randomly selected value is at least 960 dollars.
Accepted Solution
A:
Answer: 0.42Step-by-step explanation:Given: Mean : [tex]\mu=954\text{ dollars}[/tex]Standard deviation : [tex]234\text{ dollars}[/tex]Sample size : [tex]n=61[/tex]The formula to calculate z score is given by :-[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]For X=960 [tex]z=\dfrac{960 -954}{\dfrac{234}{\sqrt{61}}}=0.200262812203\approx0.2[/tex]The p-value =[tex]P(X\geq960)=1-P(X<960)=1-P(z<0.2)=1-0.5792597=0.4207403\approx0.42[/tex]Hence, the probability that a single randomly selected value is at least 960 dollars = 0.42