Question

The mean cost of a five pound bag of shrimp is 50 dollars with a variance of 64. If a sample of 43 bags of shrimp is randomly selected, what is the probability that the sample mean would differ from the true mean by greater than 1 dollar? Round your answer to four decimal places.

Answer 1

= 50

² = 64

= 8

n = 43

P( < A) = P(Z < (A - )/)

= = 50

=

=

= 1.22

P(sample mean would differ from the true mean by greater than 1 dollar) = P( < 49) or P( > 51)

= P( < 49) + 1 - P( < 51)

= P(Z < (49 - 50)/1.22) + 1 - P(Z < (51 - 50)/1.22)

= P(Z < -0.82) + 1 - P(Z < 0.82)

= 0.2061 + 1 - 0.7939

= 0.4122