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natali 33 [55]
2 years ago
14

The weight for crates of apples is normally distributed with a mean weight of 34.6 pounds and a standard deviation of 2.8 pounds

. What is the probability that the weight is between 31 and 35 pounds
Mathematics
1 answer:
Tatiana [17]2 years ago
6 0

Answer:

42.22% probability that the weight is between 31 and 35 pounds

Step-by-step explanation:

Problems of normally distributed samples are 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 problem, we have that:

\mu = 34.6, \sigma = 2.8

What is the probability that the weight is between 31 and 35 pounds

This is the pvalue of Z when X = 35 subtracted by the pvalue of Z when X = 31. So

X = 35

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

Z = \frac{35 - 34.6}{2.8}

Z = 0.14

Z = 0.14 has a pvalue of 0.5557

X = 31

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

Z = \frac{31 - 34.6}{2.8}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

0.5557 - 0.1335 = 0.4222

42.22% probability that the weight is between 31 and 35 pounds

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