55. (A) If 120 scores are chosen from a normal distribution with mean 75 and standard deviation 8, how many scores x would be expected to satisfy 67 s x s 83? (B) Use a graphing calculator to generate 120 scores from the normal distribution with mean 75 and standard de- viation 8. Determine the number of scores x such that 67 s xs 83, and compare your results with the answer to part (A).

Suppose X ~ N(3, 1.2). What value of x is two standard deviations to the right of the mean?

Suppose X ~ N(6, 2). What value of x is two standard deviations to the right of the mean?

The distribution of sample means for bi-monthly employee income at a particular company for samples of 70 employees is normal with a mean of $5921 and a standard deviation of $219. You take a random sample of 70 employees from the company and find that their mean bi-monthly income is $5668. How many standard deviations is the sample mean from the mean of the distribution of sample means?

Deandre is in his first semester at a certain university and is taking a calculus course with a large enrollment. He just took the first midterm exam and is nervous about his score. Among all of the students in the course, the mean of the exam was 67 with a standard deviation of 3. Deandre scored a 62 on this exam. (a) Find the z-score of Deandre's exam score relative to the exam scores among all the students in the course. Round your answer to two decimal places. z=0 (b) Fill in the blanks to interpret the z-score of Deandre's exam score. Make sure to express your answer in terms of a positive number of standard deviations. Deandre's exam score was standard deviations (Choose one) ▼ the mean exam score among all students in the course. Calendar ... 80 F3 F4 F6 F7 F8 F9 F10 F11 云

Directions: Solve the given problem. Show your solutions. Of all the registered automobiles in Colorado, 8% fail the state emissions test. Twelve automobiles are elected at random to undergo an emissions test. a. Find the probability that exactly four of them fail the test. b. Find the probability that fewer than four of them fail the test. c. Find the probability that more than three of them fail the test.

Suppose that the distribution of scores on an exam can be described by a normal curve with mean 110. The 16th percentile of this distribution is 80. (Use the Empirical Rule.) (a) What is the 84th percentile? (b) What is the approximate value of the standard deviation of exam scores? (c) What z score is associated with an exam score of 125? (d) What percentile corresponds to an exam score of 170? (e) Do you think there were many scores below 20? Explain. A score of 20 is? standard deviations below the mean, and so the percentage of scores below 20 would be approximately  ... how many percentage