mean = 60 wpm

standard deviation= 15 wpm

a.What is the probability that a randomly selected typist's net rate is at most 60 wpm? less than 60 wpm?

b. What is the probability that a randomly selected is between 45 and 90 wpm?

To find the probabilities in this scenario, we need to use the z-score formula and refer to the z-table. The formula for calculating the z-score is:

z = (x - μ) / σ

where:
- x is the value you want to find the probability for,
- μ is the mean of the distribution,
- σ is the standard deviation of the distribution.

Let's solve each part of the question step by step:

a. What is the probability that a randomly selected typist's net rate is at most 60 wpm?

In this case, we need to find the probability of a value being less than or equal to 60 wpm. To find this probability, we need to calculate the z-score and then look it up in the z-table.

Using the formula:
z = (60 - 60) / 15 = 0

Since the z-score is 0, we refer to the z-table to find the corresponding probability. Looking up a z-score of 0 in the table, we find that the probability is 0.5000 (or 50%).

So, the probability that a randomly selected typist's net rate is at most 60 wpm is 0.5000 or 50%.

To find the probability of a value being less than 60 wpm, we also need to consider the area to the left of 60 on the normal distribution curve. Since the area corresponding to a z-score of 0 already represents 50%, the probability of a value being less than 60 wpm is also 0.5000 or 50%.

b. What is the probability that a randomly selected typist's net rate is between 45 and 90 wpm?

To find this probability, we need to find the area under the curve between 45 and 90 wpm. In other words, we need to find the probability of a value falling between these two values.

Let's calculate the z-scores for both values:
For x = 45:
z1 = (45 - 60) / 15 = -1

For x = 90:
z2 = (90 - 60) / 15 = 2

Now, we need to find the corresponding probabilities for these z-scores in the z-table. Looking up a z-score of -1, we find that the probability is 0.1587 (or 15.87%). Similarly, a z-score of 2 corresponds to a probability of 0.9772 (or 97.72%).

Since we want to find the probability between these two z-scores, we subtract the smaller probability from the larger probability:
0.9772 - 0.1587 = 0.8185 (or 81.85%)

Therefore, the probability that a randomly selected typist's net rate is between 45 and 90 wpm is 0.8185 or 81.85%.

By using the z-score formula and referring to the z-table, we can find the probabilities in a normal distribution.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.