Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

The probability that X is less than 42 is 0.1271.

Step-by-step explanation:

The random variable X follows a Normal distribution.

The mean and standard deviation are:

E (X) = μ = 50.

SD (X) = σ = 7.

A normal distribution is continuous probability distribution.

The Normal probability distribution with mean µ and standard deviation σ is given by,

To compute the probability of a Normal random variable we first standardize the raw score.

The raw scores are standardized using the formula:

These standardized scores are known as z-scores and they follow normal distribution with mean 0 and standard deviation 1.

Compute the probability of (X < 42) as follows:

*Use a z-table for the probability.

Thus, the probability that X is less than 42 is 0.1271.

The normal curve is shown below.

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step-by-step explanation: