CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars.

Tabansi 2021-03-02 Answered

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
P(x<969)=P(x<969)=?

Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Corben Pittman
Answered 2021-03-03 Author has 83 answers

The Z-score of a random variable X is defined as follows:
Z=Xμσ
Here, μandσ are the mean and standard deviation of X, respectively.
Consider a random variable X that defines the annual cost of auto insurance.
According to the given information X follows normal distribution with mean 954 and standard deviation 271. The sample size, n is 96.
The probability that a single randomly selected value is less than 969 dollars is

P(X<969)=P((Xμ)σ<969954271)

=P(Z<0.06)=0.5221

(Using standard normal table: P(Z<0.06)=0.5221)
Therefore, the probability that a single randomly selected value is less than 969 dollars is 0.5221.

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Jeffrey Jordon
Answered 2021-11-14 Author has 2064 answers

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