Question

In: Statistics and Probability

The amount of fresh basil on the caprese salad at Olive Oil's follows a Normal distribution,...

The amount of fresh basil on the caprese salad at Olive Oil's follows a Normal distribution, with a mean of 1.15 ounces and a standard deviation of 0.21 ounce. A random sample of 14 plates of caprese salad is selected every day and the amount of basil is measured. What is the probability that the mean weight will exceed 1.23 ounces? (4 points)

Select one:

a. 0.3516

b. 0.6484

c. 0.0561

d. 0.9230

e. 0.0770

Solutions

Expert Solution

Solution :

Given that,

mean = = 1.15

standard deviation = = 0.21

n = 14

=1.15

  =  (/n) = ( 0.21 / 14  ) = 0.05612

P ( > 1.23 )

= 1 - P ( < 1.23 )

= 1 - P ( -  / ) < ( 1.23 - 1.15 / 0.05621 )

= 1 - P ( z < 0.08 / 0.05612 )

= 1 - P ( z < 1.4255 )

Using z table

= 1 - 0.9230

= 0.0770

Probability = 0.0770

Option e ) is correct.

orchestra answered 2 years ago
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