The measurement X to be taken on an individual from a population has a Normal distribution with mean u and standard deviation o. What proportion of the
individuals in the population that have their X measurements between u-20 and
u+o?
0.6826894809
0.954499876
0 0.8185946784
0 0.9973000656
O none of these

Using the normal distribution, it is found that the correct option is 0.8185946784.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which  in a set with mean and standard deviation , for 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, which is the percentile of measure X.

The proportion of measures between and is the p-value of Z when subtracted by the p-value of Z when . Thus:

has a p-value of 0.8413.

has a p-value of 0.0228.

0.8413 - 0.0228 = 0.8185.

Thus, the correct option is 0.8185946784.

A similar problem is given at

addition

step-by-step explanation: