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irina [24]
3 years ago
8

A normal distribution has a standard deviation equal to 39. What is the mean of this normal distribution if the probability of s

coring above x = 209 is 0.0228?
Mathematics
1 answer:
Naily [24]3 years ago
7 0

Answer:

The mean is \mu = 131

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:

\sigma = 39

What is the mean of this normal distribution if the probability of scoring above x = 209 is 0.0228?

This means that when X = 209, Z has a pvalue of 1-0.0228 = 0.9772. So when X = 209, Z = 2.

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

2 = \frac{209 - \mu}{39}

209 - \mu = 2*39

\mu = 209 - 78

\mu = 131

The mean is \mu = 131

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