Question

Using the Normal Distribution with Technology- Calculator Due Thursday, Sep 12, 12:59am EDT Use the Normal Distribution to compute Probability with Technology - Calculator Question The diameters of apples from a certain farm follow normal distribution with mean 4 inches and standard deviation 0.4 inch. Apples can be size-sorted by being made to roll over mesh screens. First the apples are rolled over a screen with mesh size 3.5 inches. This separates out all the apples with diameters less than 3.5 inches. Second, the remaining apples are rolled over a screen with mesh size 4.3 inches. Find the proportion of apples with diameter between 3.5 and 4.3 inches. . Round your answer to four decimal places. Provide your answer below: SUBMIT FEEDBACK MORE INSTRUCTION Content attribution

Answer 1

Answer:

65.827% of the apples have diameter between 3.5 and 4.3 inches.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

So, to find the proportion of apples with diameter between 3.5 and 4.3 inches, we subtract the pvalue of the zscore of X = 4.3 by the pvalue of the zscore of X = 3.5.

The diameters of apples from a certain farm follow normal distribution with mean 4 inches and standard deviation 0.4 inch. So $\mu = 4$, $\sigma = 0.4$.

For X = 4.3

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.3 - 4}{0.4}$

$Z = 0.75$

Z = 0.75 has a pvalue of 0.77337

For X = 3.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3.5 - 4}{0.4}$

$Z = -1.20$

Z = -1.20 has a pvalue of 0.1151

Subtracting

$0.77337 - 0.1151 = 0.65827$

65.827% of the apples have diameter between 3.5 and 4.3 inches.