Question 5 (1 point)
Factory made chocolate chip cookies will have a mean weight of 42 grams. The weight is normally distributed and for quality control, the
standard deviation is 1.5 grams. Cookies that weigh more than 45 grams or less than 39 grams are rejected. How many cookies wil be rejected
in a 5,000 count batch of cookies?

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 and standard deviation , the zscore of a measure X is given by:

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:

Proportion of rejected cookies.

Less than 39:

pvalue of Z when X = 39.

has a pvalue of 0.0228.

More than 45:

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

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.

13 is your number

Step-by-step explanation:

23 = -29 x 4x

add 29 to both sides

52 = 4x

divide both sides by 4

13 = x