The amount of marinara sauce on the spaghetti at pasta infusion follows a normal distribution, with a mean of 3.25 ounces and a standard deviation of 0.2 ounce. A random sample of 10 plates of spaghetti is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.3 ounces?

A. 0.2146

B. 0.7854

C. 0.4013

D. 0.5987

E. 0.7905

Question

Mathematics

Jasper

15 October, 17:31

The amount of marinara sauce on the spaghetti at pasta infusion follows a normal distribution, with a mean of 3.25 ounces and a standard deviation of 0.2 ounce. A random sample of 10 plates of spaghetti is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.3 ounces?

A. 0.2146

B. 0.7854

C. 0.4013

D. 0.5987

E. 0.7905

+3

Answers (1)

Know the Answer?

Ryland Cummings · Answer 1

A. 0.2146

Step-by-step explanation:

The mean and standard deviation of the sample is:

μ = 3.25

σ = 0.2 / √10 = 0.063

The z-score is:

z = (x - μ) / σ

z = (3.3 - 3.25) / 0.063

z = 0.79

The probability is therefore:

P (z > 0.79) = 0.2146