Concept explainers
(a)
Section 1:
To find: Themean for the average number of friends per user for the provided sample.
(a)
Section 1:
Answer to Problem 20E
Solution: The mean is 190friends.
Explanation of Solution
The sample mean of average number of friends per user is calculated by the formula as:
It is provided that average number of friends on Facebook for eachuser is 190and the sample of70adult users is taken. Hence, the mean of the average number of friends per adult user is 190friends.
Section 2:
To find: The sample standard deviationfor the mean number of friends per adult user.
Section 2:
Answer to Problem 20E
Solution: The sample standard deviation is
Explanation of Solution
The standard deviation of sample means is calculated by the formula as:
Hence, the sample standard deviation of mean of numbers friends per adult user is
(b)
To find: The probability that the average number of friends for 70 Facebook users is greater than 250.
(b)
Answer to Problem 20E
Solution: The probability is
Explanation of Solution
The probability that the average number of friends for 70Facebook users is greater than 250will be given by:
The probability that
The z-score for the value 250is calculated as:
The area under the curveto the right of
Therefore, the required probability that the sample of 70 Facebook users has minimum of 250 friends is
(c)
Section 1:
To find: The mean of total number of friends in the provided sample.
(c)
Section 1:
Answer to Problem 20E
Solution: The mean is27040.
Explanation of Solution
The sample mean of mean follow the approximate
And the total number of friends follows normal distribution with mean and variance as::
Hence, the mean of total number of friends in the sample is 13300.
Section 2:
To find: The standard deviation of total number of friends in the provided sample.
Section 2:
Answer to Problem 20E
Solution: The standard deviation is 288.
Explanation of Solution
The sample standard deviation of mean follow the approximate normal distribution with mean as 190and sample standard deviation as
And the total number of friends follows normal distribution with mean and variance as:
Hence, the standard deviation of total number of friends is calculated as:
(d)
To find: The probability that the total number of friends for 70Facebook users is greater than 17500.
(d)
Answer to Problem 20E
Solution: The probability is
Explanation of Solution
The required probability that the mean of total number of friends of 70users is greater than 17500; that is the required probability will be given by:
The probability that
The z-score for the value 17500is calculated as:
The area under the curve to the right of
Therefore, the obtained probability is 1.
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Chapter 5 Solutions
INTRO.TO PRACTICE STATISTICS-ACCESS
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill