The following data give the ages (in years) of all six members of a family. 57 5

ID: 3179783 • Letter: T

Question

The following data give the ages (in years) of all six members of a family.

Let x denote the age of a member of this family. What is the probability P(x=22)?

Round your answer to three decimal places.

P(x=22)=

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Consider a large population with =70 and =12. Assuming nN0.05, find the mean and standard deviation of a sample mean, x¯, for a sample size of 20.

Round your answers to three decimal places.

x¯=

A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case.

n=29

The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 6.4 minutes and a standard deviation of 4.4 minutes. Let x¯ be the mean delivery time for a random sample of 15 orders at this restaurant. Calculate the mean and standard deviation of x¯.

Round your answers to two decimal places.

The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of 0.29. Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.07 or higher.

Round your answer to four decimal places.

Explanation / Answer

a.
Mean ( u ) =6.4
Standard Deviation ( sd )= 4.4/ Sqrt(n) = 1.1361
Number ( n ) = 15
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)

b.
P(X >= 3.07) = (3.07-3.02)/0.29/ Sqrt ( 20 )
= 0.05/0.065= 0.7711
= P ( Z >0.7711) From Standard Normal Table
= 0.2203

c.
P(X < 2.9) = (2.9-3.02)/0.29/ Sqrt ( 20 )
= -0.12/0.0648= -1.8505
= P ( Z <-1.8505) From Standard NOrmal Table
= 0.032

d.
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 2.94) = (2.94-3.02)/0.29/ Sqrt ( 20 )
= -0.08/0.0648
= -1.2337
= P ( Z <-1.2337) From Standard Normal Table
= 0.10866
P(X < 3.08) = (3.08-3.02)/0.29/ Sqrt ( 20 )
= 0.06/0.0648 = 0.9253
= P ( Z <0.9253) From Standard Normal Table
= 0.82259
P(2.94 < X < 3.08) = 0.82259-0.10866 = 0.7139

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The following data give the ages (in years) of all six members of a family. 57 5

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The following data give the ages (in years) of all six members of a family. 57 5

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