Question

William averages 58 words per minute on a typing test with a standard deviation of 10.5 words per minute. Suppose William's words per minute on a typing test are normally distributed. Let X be the random variable representing the number of words per minute William types. What is the probability that William types over 70 words per minute?

A) 0.2796
B) 0.4236
C) 0.1562
D) 0.6587

Answer 1

To calculate the probability that William types over 70 words per minute, we convert his typing speed to a z-score and find the corresponding area under the normal distribution curve. We find that the probability, P(X > 70), is approximately 0.1271, which does not match any of the provided options.

Step-by-step explanation:

To find the probability that William types over 70 words per minute, we use the properties of the normal distribution. The random variable X, representing the number of words William types per minute, is normally distributed with a mean (μ) of 58 words per minute and a standard deviation (σ) of 10.5 words per minute.

To calculate the probability of typing more than 70 words per minute, we first need to determine the z-score for 70 words per minute:

Z = (X - μ) / σ

Z = (70 - 58) / 10.5 = 1.14

Now we look up the z-score of 1.14 in the standard normal distribution table or use a calculator to find the area to the right of this z-score, which gives us the probability that William types more than 70 words per minute. This area corresponds to 1 minus the cumulative probability of z = 1.14.

Using the z-table or a calculator, we find that the probability, P(X > 70), is approximately 0.1271 (which is not listed among the options provided, indicating a possible typo in the options).