# z value based probability problem

Question 1

Convert x = 70 to z-score if Normal Distribution has mean = 50

and Standard Deviation = 10.

Answer

0.5

1.0

1.5

2.0

Question 2

Using the Appendix table for standard normal distribution find the area under the curve below z = -1.25

Answer

0.1432

0.3461

0.4574

0.1056

Question 3

Find the are under standard normal distributon curve above z = 2.00

Answer

0.4572

0.0228

0.1462

0.5431

Question 4

Use standard normal distribution table (Appendix Table II)

to find the probability that z is between -1.5 and 1.5:

P(-1.5 < z < 1.5)

Answer

0.9332

0.4268

0.8664

0.0559

Question 5

For Normal distribution with mean 50 and standard deviation 10

find probability that x will be below 35.

Answer

0.8893

0.2101

0.1020

0.0668

Question 6

Household Income has Normal Distribution with average 44,000

and Standard Deviation = 20,000. Find the probability that

Household Income is GREATER than 56,000.

Answer

0.1245

0.2743

0.4184

0.6105

Question 7

Number of students who graduate College every year is Normal Distribution

with mean = 400 and standard deviation 50. Find probability that this year

between 300 and 500 students will graduate College.

Convert each number to z value and use Appendix tables B and C.

Answer

0.52

0.65

0.95

0.81

Question 8

Sample size is 64, sample mean is 50.

Assuming the population standard deviation is 16,

construct 95.44% confidence interval for population mean.

Factor z?/2=2

Answer

from 46 to 54

from 40 to 60

from 50 to 64

from 35 to 65

Question 9

For sample mean x = 80, sample size n = 36 and sample standard deviation s = 24

find 90% confidence interval for population mean.

This is the case when population standard deviation is not known,

you should use formula on page 328 with t-value from Appendix Table IV.

Tip: For confidence level 90% ? = 1 - 0.90 = 0.10, ?/2 = 0.10/2 = 0.05

In Table IV use column t0.05 and line with df = n - 1 = 36 - 1 = 35.

Answer

from 65.48 to 95.86

from 75.44 to 82.16

from 73.24 to 86.76

from 70.18 to 88.65

#### Solution Preview

Hi there,

Thanks for your understanding. Here are my answers:

Hi there,

Thanks for allowing me to work on your questions.

1. z=(x-mean)/standard deviation=(70-50)/10=2.

2. find the area under the curve below z = -1.25

Answer 0.1056

3. Find the are under standard ...

#### Solution Summary

This solution provides some detailed explanation how to use z value to find out the probability.