Answer:
The cutoff numbers for the number of chocolate chips in acceptable cookies are 16.242 and 27.758
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 problem, we have that:
Middle 90%
Between the 50 - (90/2) = 5th percentile to the 50 + (90/2) = 95th percentile.
5th percentile:
X when Z has a pvalue of 0.05. So X when Z = -1.645.
95th percentile:
X when Z has a pvalue of 0.95. So X when Z = 1.645.
The cutoff numbers for the number of chocolate chips in acceptable cookies are 16.242 and 27.758