Jackson is interested in the number of memories people can recall. He knows that the number of memories recalled is normally distributed in the general population, with a population mean of 30 and a population standard deviation of 5. What is the probability that Jackson randomly selects a person from this population who recalls between 26 and 29 memories

0.2088 = 20.88% probability that Jackson randomly selects a person from this population who recalls between 26 and 29 memories.

Step-by-step explanation:

Normal Probability Distribution:

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

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

Population mean of 30 and a population standard deviation of 5.

This means that

What is the probability that Jackson randomly selects a person from this population who recalls between 26 and 29 memories?

This is the pvalue of Z when X = 29 subtracted by the pvalue of Z when X = 26. So

X = 29

has a pvalue of 0.4207

X = 26

has a pvalue of 0.2119

0.4207 - 0.2119 = 0.2088

0.2088 = 20.88% probability that Jackson randomly selects a person from this population who recalls between 26 and 29 memories.

2x^2+5x+17

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