Question

The mileage of the hybrid car, the Honda Insight, is normally distributed with a mean of 63.4 mpg and a standard deviation of 12.6 mpg.

1. Is it possible to find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg? Provide a justification for your answer.

2. If we want to address the problem “Find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg”, write the probability statement.

3. If we want to address the problem “Find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg”, what is the probability? Be sure to show how you calculated your probability.

Answer 1

we are given x : mileage of hybrid car is normally distributed with mean = 63.4 and standard deviation

=12.6

If x is normally distributed then sampling distribution of xbar is mean xbar = 63.4 and standard deviation xbar = / n = 12.6/7 = 4.76

So this is possible to find probability that the mean mileage of seven Honda Insights exceed 70 mpg

2) probability statement P(xbar > 70)

3) P( xbar > 70 ) = P( (xbar - ) /(/n) > 70 - / /n)

= P( Z >( 70- 63.4) /4.76)

= P( Z > 1.39)

= 1 - P( Z < 1.39)

P( xbar > 70) = 1 - 0.9177

P( xbar > 70) = 0.0823