## Assume that the random variable X is normally​ distributed, with mean mu equals 80μ=80 and standard deviation sigma equals 20.σ=20. Compute

Question

Assume that the random variable X is normally​ distributed, with mean mu equals 80μ=80 and standard deviation sigma equals 20.σ=20. Compute the probability ​P(Xgreater than>9696​).

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7 months 2021-10-08T00:29:51+00:00 1 Answer 0 views 0

$$P(X \geq 86) = 1 – 0.7881 = 0.2119$$

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:

$$\mu = 80, \sigma = 20$$

Compute the probability ​P(Xgreater than>96​).

This is 1 subtracted by the pvalue of Z when X = 96. So

$$Z = \frac{X – \mu}{\sigma}$$

$$Z = \frac{96 – 80}{20}$$

$$Z = 0.8$$

$$Z = 0.8$$ has a pvalue of 0.7881

$$P(X \geq 86) = 1 – 0.7881 = 0.2119$$