What are the characteristics of a normal distributions? What is the standard nor

Question

What are the characteristics of a normal distributions? What is the standard normal distribution important in statistical analysis? What is the total area under the standard normal distribution curve? What percentage of the area falls below the mean? Above the mean? About what percentage of the area under the normal distribution curve falls within 1 standard deviation above and below the mean? 2 standard deviations? What are two other names for a normal distribution? For Exercise 7 through 26, find the area under the standard normal distribution curve. Between z = 0 and z = 0.98 Between z = 0 and z = 1.77 Between z = 0 and z = -2.14 Between z = 0 and z = -0.32 To the right of z = 0.29 To the right of z = 2.01 To the left of z = -1.39 Between z = 1.09 and z = 1.83 (0.2266) Between z = 1.56 and z = -1.83 (0.0258) Between z = -1.46 and z = -1.98 (0.0482) To the left of z = 2.22 (0.9868) To the right of z = -0.12 (0.5478) To the right of z = 1.92 and to the left of z = -0.44 (0.3574) Find the probability for each, using the standard normal distribution P (0

Explanation / Answer

11. To the right of Z = 0.29:

Since Z is positive, it is on RHS of mid value.

From Table, corresponding to Z = 0.29, area = 0.1141.

This is the area from mid point to Z = 0.29.But, since to the right of Z = 0.29 is required,

P(Z > 0.29) = 0.5 - 0.1141 =0.3859

13. To the left of Z = - 1.39.

Since Z is negative , it is on LHS of mid value.

From Table, corresponding to Z = 1.39, area = 0.4177.

This is the area from mid value to Z = -1.39 lying on the left of mid value. But, to the left of Z = - 1.39 is required.

So, P(X < - 1.39) = 0.5 - 0.4177 = 0.0823

15. Between Z = 1.09 and Z = 1.83

From table, corresponding areas are: 0.3621 and 0.0.4663.

So, P(1.09 < Z < 1.83) = 0.4664 - 0.3621 = 0.1043

17. Between Z = - 1.56 and Z = - 1.83

Since both Z values are negative, the are LHS of mid value.

From Table, corresponding areas are : 0.4406 and 0.4664.

So, P(- 1.83 < Z < - 1.56) = 0.0258

19. P(between - 1.46 and - 1.98):

Since both Z values are negative, they are on LHS of mid value.

From Table, corresponding areas are: 0.4279 and 0.4761.

So, P( - 1.98 < X < - 1.46) = 0.4761 - 0.4279 = 0.0482

21. To the left of Z = 2.22

Since Z is positive, it is on RHS of mid value.

Area corresponding to Z = 2.22 is 0.4868.

So, To the left of Z = 2.22 is 0.5 + 0.4868 = 0.9868

SINCE THE QUESTIONS ARE LARGE, ONLY FIRST 4 QUESTIONS ARE ANSWERED AS PER DIECTIONS FOR ANSWERING.

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