A market research company employs a large number of typists to enter data into a computer. The time taken for new typists to learn the computer system is known to have a normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. The proportion of new typists that take at most two hours to learn the computer system is

The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of 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. 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.

Normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes.

This means that

The proportion of new typists that take at most two hours to learn the computer system is

This is the pvalue of Z when X = 120 minutes = 2 hours. So

has a pvalue of 0.9525.

The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.

(x+3)(x+7)

step-by-step explanation: