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Ronch [10]
3 years ago
8

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3408 miles, with a variance

of 249,001. If he is correct, what is the probability that the mean of a sample of 36 cars would be less than 3245 miles
Mathematics
1 answer:
Murrr4er [49]3 years ago
6 0

Answer:

The probability that the mean of a sample of 36 cars would be less than 3245 miles

P(X⁻≤3245) = 0.975

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

The mean number of miles between services

                   μ= 3408 miles  

The Variance of miles between services

                σ² = 249,001

                σ = √249,001 = 499

Let 'X' be a random variable in a normal distribution

Given sample size 'n' =36

<u><em>Step(ii):</em></u>-

           Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }

          Z = -163/83.16 = 1.96

The probability that the mean of a sample of 36 cars would be less than 3245 miles

P(X⁻≤3245)  =   P(Z≤1.96)

                   =   0.5 + A(1.96)

                   =  0.5 + 0.4750

                  =   0.975

<u><em>Final answer</em></u>:-

The probability that the mean of a sample of 36 cars would be less than 3245 miles

P(X⁻≤3245) =0.975

           

         

         

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