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Use the information in Example 7.8, but use a sample size of 55 to answer the following questions. a. Find P( x ¯ < 7).

b. Find P(Σx > 170).

c. Find the 80th percentile for the mean of 55 scores.

d. Find the 85th percentile for the sum of 55 scores.

Short Answer

Expert verified

a) P(x<7)-1

b) P(x>170)-0.2788)

c) k1-3.13

d)k2-174.8393

Step by step solution

01

Part (a) step: 1 Given Information

We have given that the sample size of 55.

We need to findP(x<7)-1.

02

Part(a) step: 2 Simplify

P(x<7)

We have

normalcdf1,7,3,1.1555-1

The probability that the mean stress score is less than 7is 1.

Normal Distribution:

03

Part (b) step: 1 Given Information  

We have given that the sample size of 55.

We need to find that P(x>170).

04

Part (b) Step: 2 simplify 

P(x>170)

We have

normalcdf(170,1E99,55×355×1.15)

The probability that the total of 55scores is more than 170is 0.2788.

Normal Distribution:

05

Part (c) Step: 1 Given information 

We have given that the sample size of 55.

We need to find that the80thpercentile.

06

Part (c) step: 2 Simplify

Let k1-the 80thpercentile

We need to find P{x<k1)-0.80:

invNorm0.80,3,1.1555-3.1'3

The 80thpercentile for the mean of 55score is about 3.13.

This tells us about80%of all the means of55stress scores are at most3.13and that20%are at least3.13.

07

Part (d) step : 1 Given information 

We heve given that the sample size of 55.

We need to find that85thpercentile.

08

Part (d) Step:2 Simplify

Let k2-the 85thpercentile

We need to find Px<k2-0.85

invNorm(0.85,55×3,55×1.15)-173.8393.

The 85thpercentile for the sum of 55scores is about 173.8393.

This tells us that 85thof all the sums of55scores are no more than173.8393and15%are no less than173.8393.

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Most popular questions from this chapter

Find the probability that the sum of the 100 values falls between the numbers you found in and.

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RedOrangeYellowBrownBlueGreen
0.751
0.735
0.883
0.696
0.881
0.925
0.841
0.895
0.769
0.876
0.863
0.914
0.856
0.865
0.859
0.855
0.775
0.881
0.799
0.864
0.784
0.8060.854
0.865
0.966
0.852
0.824
0.840
0.810
0.865
0.859
0.866
0.858
0.868
0.858
1.015
0.857
0.859
0.848
0.859
0.818
0.876
0.942
0.838
0.851
0.982
0.868
0.809
0.873
0.863


0.803
0.865
0.809
0.888


0.932
0.848
0.890
0.925


0.842
0.940
0.878
0.793


0.832
0.833
0.905
0.977


0.807
0.845

0.850


0.841
0.852

0.830


0.932
0.778

0.856


0.833
0.814

0.842


0.881
0.791

0.778


0.818
0.810

0.786


0.864
0.881

0.853


0.825


0.864


0.855


0.873


0.942


0.880


0.825


0.882


0.869


0.931


0.912





0.887

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