The heights of 500 students are normally distributed with a mean of 162.5 centimeters and a standard deviation of 7.6 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would be expected to have heights (a) less than 149.0 centimeters? (b) between 160.5 and 171.0 centimeters inclusive? (c) equal to 163.0 centimeters? (d) greater than or equal to 177.0 centimeters? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) 19 student(s) (Round to the nearest whole number as needed.)
The heights of 500 students are normally distributed with a mean of 162.5 centimeters and a standard deviation of 7.6 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would be expected to have heights (a) less than 149.0 centimeters? (b) between 160.5 and 171.0 centimeters inclusive? (c) equal to 163.0 centimeters? (d) greater than or equal to 177.0 centimeters? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) 19 student(s) (Round to the nearest whole number as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 31PPS
Related questions
Question
I need help with parts b through d please
![Areas under the Normal Curve
Areas under the Normal Curve
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z
Z
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0.3
0.4
-0.3 0.3821 0.3783 0.3745
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0.3483 -0.3
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0.0084 -2.3
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2
.00
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2.3
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2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
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0.5319 0.5359 0.0
2
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Transcribed Image Text:Areas under the Normal Curve
Areas under the Normal Curve
z
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.01
-3.4
0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004
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.09
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0.0005 0.0005 -3.2
z
Z
.00
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.07
0.0007 0.0007 -3.1
0.0010 0.0010 -3.0
0.3
0.4
-0.3 0.3821 0.3783 0.3745
2
.00
.01
0.0041 0.0040 0.0039 0.0038
0.0055 0.0054 0.0052 0.0051
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0.3707 0.3669 0.3632 0.3594 0.3557
0.3483 -0.3
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.02
.03
.04
.05
.06
.07
.08
.09
Z
0.0014 0.0014 -2.9
0.0020 0.0019 -2.8
0.0027 0.0026 2.7
0.0037 0.0036 -2.6
0.0049 0.0048 -2.5
0.5
0.0084 -2.3
0.0110 -2.2
0.0143 -2.1
2.7
0.2483 0.2451 -0.6
0.2810
0.2776 -0.5
0.3156
0.3520
0.3121 -0.4
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2
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0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.6179 0.6217 0.6255
0.6293 0.6331
0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0.9783 0.9788 0,9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878
0.9881 0.9884 0.9887 0.9890 2.2
2.3
0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.6
0.9965 0.9966 0.9967
0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992
0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993
0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
.01
.02
.03
.04
.05
.06
.07
.08
.09
.08
.09
0.5319 0.5359 0.0
2
Z
![The heights of 500 students are normally distributed with a mean of 162.5 centimeters and a standard deviation of
7.6 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students
would be expected to have heights
(a) less than 149.0 centimeters?
(b) between 160.5 and 171.0 centimeters inclusive?
(c) equal to 163.0 centimeters?
(d) greater than or equal to 177.0 centimeters?
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
(a) 19 student(s)
(Round to the nearest whole number as needed.)
(b) ☐ student(s)
(Round to the nearest whole number as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56c5e78b-efea-4050-aee5-21b7649ec467%2Fac252892-f6e5-4224-a2d4-2678e373c6f4%2Faouiz9p_processed.png&w=3840&q=75)
Transcribed Image Text:The heights of 500 students are normally distributed with a mean of 162.5 centimeters and a standard deviation of
7.6 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students
would be expected to have heights
(a) less than 149.0 centimeters?
(b) between 160.5 and 171.0 centimeters inclusive?
(c) equal to 163.0 centimeters?
(d) greater than or equal to 177.0 centimeters?
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
(a) 19 student(s)
(Round to the nearest whole number as needed.)
(b) ☐ student(s)
(Round to the nearest whole number as needed.)
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