Question

Assume that the random variable X is normally distributed, with mean μ = 110 and standard deviation σ = 20. Compute the probability P(X > 126).

Answer 1

Answer:

P(X > 126) = 0.2119

Step-by-step explanation:

Problems of normally distributed samples can be 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:

$\mu = 110, \sigma = 20$

P(X > 126) is the 1 subtracted by the pvalue of Z when X = 126. So

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

$Z = \frac{126 - 110}{20}$

[tez]Z = 0.8[/tex]

[tez]Z = 0.8[/tex] has a pvalue of 0.7881.

P(X > 126) = 1 - 0.7881 = 0.2119