Question

Cucumbers grown on a certain farm have weights with a standard deviation of 2 ounces. What is the mean weight if 85% of the cucumber weigh less than 16 ounces

Answer 1

Answer:

The mean weight of cucumbers is 13.94 ounces.

Step-by-step explanation:

Assume that the weights of the cucumbers (X) follows a normal distribution.

Given:

Standard deviation (σ) = 2 ounces

P (X < 16) = 0.85

Compute the z-score as follows:

$P(X<16) = 0.85\\Then,\\P(\frac{X-\mu}{\sigma} < \frac{16-\mu}{\sigma}) = 0.85\\ P(Z<z)=0.85$

Use the standard normal table to determine the z-score.

The value of z is 1.03.

Compute the mean weight of cucumbers as follows:

$\frac{16-\mu}{2}=1.03 \\16-\mu=2.06\\\mu=13.94$

Thus, the mean weight of cucumbers is 13.94 ounces.