Question

Question 5 (1 point)

Answer 1

Answer:

228 cookies wil be rejected in a 5,000 count batch of cookies.

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:

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

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu = 42, \sigma = 1.5$

Proportion of rejected cookies.

Less than 39:

pvalue of Z when X = 39.

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

$Z = \frac{39 - 42}{1.5}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

More than 45:

1 subtracted by the pvalue of Z when X = 45.

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

$Z = \frac{45 - 42}{1.5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

Total:

2*0.0228 = 0.0456

How many cookies wil be rejected in a 5,000 count batch of cookies?

The proportion of cookies rejected is 0.0456. Out of 5000:

0.0456*5000 = 228

228 cookies wil be rejected in a 5,000 count batch of cookies.