A random sample of size 25 is taken from a normal population having a mean of 85 and a standard deviation of 2. A second random sample of size 81 is taken from a different normal population having a mean of 75 and a standard deviation of 6. Find the probability that the sample mean computed from the 25 measurements will exceed the sample mean computed from the 81 measurements by at least 8.7 but less than 10.6. Assume the difference of the means to be measured to the nearest tenth. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The probability is (Round to four decimal places as needed.)
A random sample of size 25 is taken from a normal population having a mean of 85 and a standard deviation of 2. A second random sample of size 81 is taken from a different normal population having a mean of 75 and a standard deviation of 6. Find the probability that the sample mean computed from the 25 measurements will exceed the sample mean computed from the 81 measurements by at least 8.7 but less than 10.6. Assume the difference of the means to be measured to the nearest tenth. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The probability is (Round to four decimal places as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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- [Click here to view page 2 of the standard normal distribution table.](#)
**Solution:**
- The probability is __.
- (Round to four decimal places as needed.)
---
This problem involves finding probabilities related to the difference in sample means from two different populations. To solve this, you will need to use statistical methods and standard normal distribution tables. The linked resources provide the necessary tables to aid in calculating the probability. Ensure all calculations involving the means and standard deviations are done accurately and round your final probability to four decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7167d01a-fc0a-4c3f-ab49-29dc29956a80%2Fa04a7eeb-c725-4fef-a3ab-7005f6f6f28d%2Fl745ci9_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Probability Problem**
*A random sample of size 25 is taken from a normal population having a mean of 85 and a standard deviation of 2. A second random sample of size 81 is taken from a different normal population having a mean of 75 and a standard deviation of 6. Find the probability that the sample mean computed from the 25 measurements will exceed the sample mean computed from the 81 measurements by at least 8.7 but less than 10.6. Assume the difference of the means to be measured to the nearest tenth.*
**Helpful Resources:**
- [Click here to view page 1 of the standard normal distribution table.](#)
- [Click here to view page 2 of the standard normal distribution table.](#)
**Solution:**
- The probability is __.
- (Round to four decimal places as needed.)
---
This problem involves finding probabilities related to the difference in sample means from two different populations. To solve this, you will need to use statistical methods and standard normal distribution tables. The linked resources provide the necessary tables to aid in calculating the probability. Ensure all calculations involving the means and standard deviations are done accurately and round your final probability to four decimal places.
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