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andre [41]
3 years ago
6

A particular fruit's weights are normally distributed, with a mean of 275 grams and a standard deviation of 19 grams. If you pic

k one fruit at random, what is the probability that it will weigh between 244 grams and 305 grams?
Mathematics
1 answer:
lakkis [162]3 years ago
6 0

Answer:

0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 275 grams and a standard deviation of 19 grams

This means that \mu = 275, \sigma = 19

What is the probability that it will weigh between 244 grams and 305 grams?

This is the p-value of Z when X = 305 subtracted by the p-value of Z when X = 244.

X = 305

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

Z = \frac{305 - 275}{19}

Z = 1.58

Z = 1.58 has a p-value of 0.9429.

X = 244

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

Z = \frac{244 - 275}{19}

Z = -1.63

Z = -1.63 has a p-value of 0.0516

0.9429 - 0.0516 = 0.8913

0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.

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