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## 1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

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1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

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Mathematics
3 years
2021-07-22T10:33:26+00:00
2021-07-22T10:33:26+00:00 1 Answers
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## Answers ( )

Answer:0.6826 = 68.26% probability that you have values in this interval.

Step-by-step explanation:Normal Probability DistributionProblems 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.

X~N(8, 1.5)This means that

What is the probability that you have values between (6.5, 9.5)?This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So

X = 9.5has a p-value of 0.8413.

X = 6.5has a p-value of 0.1587

0.8413 – 0.1587 = 0.6826

0.6826 = 68.26% probability that you have values in this interval.