For a normal distribution, which of these are roughly the same? (a) mean; varian

Question

For a normal distribution, which of these are roughly the same? (a) mean; variance (c) mean mode; median (d) median standard deviation For the standard normal distribution, which of these equals 1? (a) mean (c) median For the standard normal distribution, which of these equals 0? (a) mean (c) median For exercises (16) through (25) use the following graph image (13) (b) mode; standard deviation (14) (b) standard deviation (d) varlance (15) (b) (d) standard deviation Both (a) and (c) 34.13% | 34.13% 2.28% 13.59% 13.59% 2.28% About 68% -About 95% About 99.7% (16) The area within 1 standard deviation from the mean is about 95 % . (a) True (b) False (17) The area within 2 standard deviations from the mean is about 99.7 % . (a) True (b) False (18) The area from z 0 to z- 1 is about 68 % . (19) The area from z 0 to z--1 is about 68 % . (20) The area from z 1 to z = -1 is about 68 % . (21) The area within 3 standard deviations from the mean is about 99.7%. (a) True (b) Faise (22) The area from z #0toz#+5is about 50 % (23) The area from z =-5to z =5?s about 100 % (24) The area from z--2to z#lis about 81.85 % (25) The area from z =-1to z=2isabout 81.85 % (a) True (b) False (a) True (b) False (a) True (b) False (a) True (b) Faise (a) True (b) False (a) True (b) False (a) True (b) False

Explanation / Answer

13) Option - c) mean, mode, median

14) Option - b) standard deviation.

15) Option - a) mean

16) Option - b) False

The area within 1 standard deviation from the mean is about 68%.

17) Option - b) False

The area within 2 standard deviation from the mean is about 95%.

18) P(0 < Z < 1)

= P(Z < 1) - P(Z < 0)

= 0.8413 - 0.5

= 0.3413 = 34.13%

Option - b) False

19) P(-1 < Z < 0)

= P(Z < 0) - P(Z < -1)

= 0.5 - 0.1587

= 0.3413

= 34.13%

Option - b) False

20) P(1- < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826 = 68.26%

Option - a) True

21) Option - a) True

22) P(0 < Z < 5)

= P(Z < 5) - P(Z < 0)

= 1 - 0.5

= 0.5 = 50%

Option - a) True

23) P(-5 < Z < 5)

= P(Z < 5) - P(Z < -5)

= 1 - 0 = 1 = 100%

Option - a) True

24) P(-2 < Z < 1)

= P(Z < 1) - P(Z < -2)

= 0.8413 - 0.0228

= 0.8185 = 81.85%

Option - a) True

25) P(-1 < Z < 2)

= P(Z < 2) - P(Z < -1)

= 0.9772 - 0.1587

= 0.8185 = 81.85%

Option - a) True

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