Question

Johnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives...

Johnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives of these tubes is 135 hours. The company’s research department takes a sample of 105 such tubes and finds that the mean life of these tubes is 2150 hours. What is the probability that this sample mean is within 20 hours of the mean life of all tubes produced by this company?



Round your answer to four decimal places.

P=___

Homework Answers

Answer #1

Here, μ = 2150, σ = 135/sqrt(105) = 13.1747, x1 = 2130 and x2 = 2170. We need to compute P(2130<= X <= 2170). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (2130 - 2150)/13.1747 = -1.52
z2 = (2170 - 2150)/13.1747 = 1.52

Therefore, we get
P(2130 <= X <= 2170) = P((2170 - 2150)/13.1747) <= z <= (2170 - 2150)/13.1747)
= P(-1.52 <= z <= 1.52) = P(z <= 1.52) - P(z <= -1.52)
= 0.9357 - 0.0643
= 0.8714

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Future Electronics makes compact disc players. Its research department found that the life of the laser...
Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 5020 hours and standard deviation 400 hours. (a) Find the probability that the laser beam device will wear out in 5000 hours or less. (Round your answer to four decimal places.) (b) Future Electronics wants to place a guarantee on the players so that no more than 4% fail during the guarantee period. Because the laser pickup...
Future Electronics makes compact disc players. Its research department found that the life of the laser...
Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 4740 hours and standard deviation 460 hours. (a) Find the probability that the laser beam device will wear out in 5000 hours or less. (Round your answer to four decimal places.) (b) Future Electronics wants to place a guarantee on the players so that no more than 10% fail during the guarantee period. Because the laser pickup...
Future Electronics makes compact disc players. Its research department found that the life of the laser...
Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 5020 hours and standard deviation 450 hours. (a) Find the probability that the laser beam device will wear out in 5000 hours or less. (Round your answer to four decimal places.) _______ (b) Future Electronics wants to place a guarantee on the players so that no more than 10% fail during the guarantee period. Because the laser...
Future Electronics makes compact disc players. Its research department found that the life of the laser...
Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 4940 hours and a standard deviation of 480 hours. (a) Find the probability that the laser beam device will wear out in 5000 hours or less. (b) Future Electronics wants to place a guarantee on the players so that no more than 13% fail during the guarantee period. Because the laser pickup is the part most likely...
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine...
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed and vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.035 inch. The quality...
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine...
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed and vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.035 inch. The quality...
1) The average life of light bulbs produced by SABA Electric Co. is expected to be...
1) The average life of light bulbs produced by SABA Electric Co. is expected to be normally distributed with the mean service life of 850 hours and a standard deviation of 100 hours. A random sample of 144 bulbs is tested and it has a mean life of 920 hours. Can it be concluded that the mean service life of the bulbs is more than the expectation at significant level of 0.02? 1) Which method researcher can use to check...
1. According to the Bureau labor of statistics, the mean weekly earnings for people working in...
1. According to the Bureau labor of statistics, the mean weekly earnings for people working in a sales-related profession in 2010 was $660. Assume the weekly earnings are approximately normally distributed with a standard deviation of $75. If a salesperson was randomly selected, find the probability that his or her weekly earnings are at most $40.(choose the best answer) a. .0004 b. .4246 c. .0478 d. .4182 e. .6255 2. A film distribution manager calculates that 8% of the films...
1. Find the area under the standard normal curve (round to four decimal places) a. To...
1. Find the area under the standard normal curve (round to four decimal places) a. To the left of  z=1.65 b. To the right of z = 0.54 c. Between z = -2.05 and z = 1.05 2. Find the z-score that has an area of 0.23 to its right. 3. The average height of a certain group of children is 49 inches with a standard deviation of 3 inches. If the heights are normally distributed, find the probability that a...
2. SECURING THE WORKFORCE Diversity management in X-tech, a Japanese organisation This case is intended to...
2. SECURING THE WORKFORCE Diversity management in X-tech, a Japanese organisation This case is intended to be used as a basis for class discussion rather than as an illustration of the effective or ineffective handling of an administrative situation. The name of the company is disguised. INTRODUCTION In light of demographic concerns, in 2012, the Japanese government initiated an effort to change the work environment in order to secure the workforce of the future. Japan is world renowned for its...