Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 42, \sigma = 1.5[/tex]
Proportion of rejected cookies.
Less than 39:
pvalue of Z when X = 39.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{39 - 42}{1.5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228.
More than 45:
1 subtracted by the pvalue of Z when X = 45.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 42}{1.5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] 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.
