Relax! A recent survey asked 1682 people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 0 113 1 184 2 336 3 251 4 318 5 234 6 151 7 35 8 60 Total 1682 Send data to Excel Consider these 1682 people to be a population. Let X be the number of hours of relaxation for a person sampled at random from this population. Part 1 of 5 (a) Construct the probability distribution of X . Round the answer to three decimal places. x 0 1 2 3 4 5 6 7 8 P ( x ) Part 2 of 5 (b) Find the probability that a person relaxes more than 4 hours per day. The probability that a person relaxes more than 4 hours per day is .( Round the answer to three decimal places.) Part 3 of 5 (c) Find the probability that a person doesn't relax at all. The probability that a person doesn't relax at all is .( Round the answer to three decimal places.) Part 4 of 5 (d) Compute the mean μx . Round the answer to two decimal places. μx = Part 5 of 5 (e) Compute the standard deviation σx . Round the answer to three decimal places. σx =
Relax! A recent survey asked 1682 people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 0 113 1 184 2 336 3 251 4 318 5 234 6 151 7 35 8 60 Total 1682 Send data to Excel Consider these 1682 people to be a population. Let X be the number of hours of relaxation for a person sampled at random from this population. Part 1 of 5 (a) Construct the probability distribution of X . Round the answer to three decimal places. x 0 1 2 3 4 5 6 7 8 P ( x ) Part 2 of 5 (b) Find the probability that a person relaxes more than 4 hours per day. The probability that a person relaxes more than 4 hours per day is .( Round the answer to three decimal places.) Part 3 of 5 (c) Find the probability that a person doesn't relax at all. The probability that a person doesn't relax at all is .( Round the answer to three decimal places.) Part 4 of 5 (d) Compute the mean μx . Round the answer to two decimal places. μx = Part 5 of 5 (e) Compute the standard deviation σx . Round the answer to three decimal places. σx =
Relax! A recent survey asked 1682 people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 0 113 1 184 2 336 3 251 4 318 5 234 6 151 7 35 8 60 Total 1682 Send data to Excel Consider these 1682 people to be a population. Let X be the number of hours of relaxation for a person sampled at random from this population. Part 1 of 5 (a) Construct the probability distribution of X . Round the answer to three decimal places. x 0 1 2 3 4 5 6 7 8 P ( x ) Part 2 of 5 (b) Find the probability that a person relaxes more than 4 hours per day. The probability that a person relaxes more than 4 hours per day is .( Round the answer to three decimal places.) Part 3 of 5 (c) Find the probability that a person doesn't relax at all. The probability that a person doesn't relax at all is .( Round the answer to three decimal places.) Part 4 of 5 (d) Compute the mean μx . Round the answer to two decimal places. μx = Part 5 of 5 (e) Compute the standard deviation σx . Round the answer to three decimal places. σx =
people how many hours per day they were able to relax. The results are presented in the following table.
Number of Hours
Frequency
0
113
1
184
2
336
3
251
4
318
5
234
6
151
7
35
8
60
Total
1682
Send data to Excel
Consider these 1682 people to be a population. Let
X
be the number of hours of relaxation for a person sampled at random from this population.
Part 1 of 5
(a) Construct the probability distribution of
X
. Round the answer to three decimal places.
x
0
1
2
3
4
5
6
7
8
P
(
x
)
Part 2 of 5
(b) Find the probability that a person relaxes more than
4
hours per day.
The probability that a person relaxes more than
4
hours per day is
.( Round the answer to three decimal places.)
Part 3 of 5
(c) Find the probability that a person doesn't relax at all.
The probability that a person doesn't relax at all is
.( Round the answer to three decimal places.)
Part 4 of 5
(d) Compute the mean
μx
. Round the answer to two decimal places.
μx
=
Part 5 of 5
(e) Compute the standard deviation
σx
. Round the answer to three decimal places.
σx
=
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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