Question

The weight for crates of eggs is normally distributed with a mean weight of 34.6 pounds and a standard deviation of 2.8 pounds. What is the probability that the weight is between 31 and 35.7 pounds?

Answer 1

0.5532

Explanation:

The probability of an event is defined to be the ratio of the number of cases favourable to the event—i.e., the number of outcomes in the subset of the sample space defining the event—to the total number of cases.

Please kindly refer to attachment for the step by step solution.

Answer 2

0.5532

Explanation:

P( 31<X<35.7)

P(X>31)= P(Z>(31-μ)/σ)

= P(Z>(31-34.6)/2.8)

= P(Z> -1.2857)

P(X<35.7)= P(Z<(35.7-μ)/σ)

= P(Z<(35.7-34.6)/2.8)

=P(Z< 0.392857)

From z-distribution table

P(Z< -1.29)= 0.09853

p(Z< 0.39) = 0.65173

P( 31<X<35.7)= P(Z<0.39)- P(Z<-1.29)

= 0.65173- 0.09853

=0.5532