Question

The cost of 5 gallons of ice cream has a variance of 36 with a mean of 36

dollars during the summer.

What is the probability that the sample mean would differ from the true mean by more than  0.6

  dollars if a sample of 107

  5-gallon pails is randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 6 / $\sqrt$ 107 = 0.5800

= 1 - P[(-0.6) / 0.5800 < ($\bar x$ - $\mu$ _{$\bar x$}) / $\sigma$ _{$\bar x$} < (0.6) / 0.5800)]

= 1 - P(-1.03 < Z < 1.03)

= 1 - P(Z < 1.03) - P(Z < -1.03)

= 1 - P(0.8485 - 0.1515)

= 1 - 0.697

= 0.3030

Probability = 0.3033