Question

Parts A-D

A)On average, a student takes 130 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 10 words/minute, find the probability that a student randomly selected from the course can take dictation at the following speeds. (Round your answers to four decimal places.)

(1) more than 150 words/minute______


(2) between 100 and 150 words/minute________


(3) less than 100 words/minute_________

B)The tread lives of the Super Titan radial tires under normal driving conditions are normally distributed with a mean of 30,000 mi and a standard deviation of 5000 mi. (Round your answers to four decimal places.)

(1)What is the probability that a tire selected at random will have a tread life of more than 24,500 mi?_________


(2)Determine the probability that four tires selected at random still have useful tread lives after 24,500 mi of driving. (Assume that the tread lives of the tires are independent of each other.)_________

C)Let Z be the standard normal variable. Find z if z satisfies the given value. (Round your answer to two decimal places.)

P(Z < z) = 0.1210

(1)z=_________

D)Let Z be the standard normal variable. Find z if z satisfies the given value. (Round your answer to two decimal places.)

P(Z > z) = 0.9878

(1)z=_______

Answer 1

(A) We have to find the z-scores corresponding to the given x-values:-

we know that the mean is 130, and the standard deviation is 10. So the z-score is given by the formula

Now, the z score for x = 150 is

Now, we can find the probability of z from 0 to z using a standard normal distribution table, which gives it as

So, the required probability is

Now, we have to find the z score for x = 100, which is

Now, this z score gives us a probability of 0.4987, so adding it to the probability of z=150, that is, 0.4772, we have

Now, we already know the probability of the z score = -3 corresponding to x = 100, so we just have to find the probability of z being lower than this, which is simply

Thus, the answers are:-

The probability that a student can take dictation at

(1) more than 150 words per minute = 0.0228 = 2.28%

(2) between 100 and 150 words per minute = 0.9759 = 97.59%

(3) less than 100 words per minute = 0.0013 = 0.13%