# Thread: Normal Distribution

1. ## Normal Distribution

1. If Y has a normal distribution with mean 90 and SD 20, find the following probabilities.
a. P(|Y – 90| < 2)

b. P(|Y(bar) - 90| < 2) if Y(bar) is a random sample of 25 Yi’s from the normal distribution above.

c. P(|Y(bar) - 90| < 2) if Y(bar) is a random sample of 100 Yi’s from the normal distribution above.

d. P(|Y(bar) - 90| < 2) if Y(bar) is a random sample of 900 Yi’s from the normal distribution above.

e. Which of the probabilities in a through d is most affected by dropping the assumption that Y has a normal distribution, but maintaining the assumptions that the mean is 90 and the SD is 20? Which is least affected? Why?
f. The weak law of large numbers says what about limn → ∞ P(|Y(bar) - 90| < 2)?
g. In problem 1d, find P(| - 90)| < .01.
h. Do you draw any different conclusion for limn → ∞ P(|Y(bar) - 90| < .01) than you do in 1f?

2. Originally Posted by ShaunW
1. If Y has a normal distribution with mean 90 and SD 20, find the following probabilities.
a. P(|Y – 90| < 2)

b. P(|Y(bar) - 90| < 2) if Y(bar) is a random sample of 25 Yi’s from the normal distribution above.

c. P(|Y(bar) - 90| < 2) if Y(bar) is a random sample of 100 Yi’s from the normal distribution above.

d. P(|Y(bar) - 90| < 2) if Y(bar) is a random sample of 900 Yi’s from the normal distribution above.

e. Which of the probabilities in a through d is most affected by dropping the assumption that Y has a normal distribution, but maintaining the assumptions that the mean is 90 and the SD is 20? Which is least affected? Why?
f. The weak law of large numbers says what about limn → ∞ P(|Y(bar) - 90| < 2)?
g. In problem 1d, find P(| - 90)| < .01.
h. Do you draw any different conclusion for limn → ∞ P(|Y(bar) - 90| < .01) than you do in 1f?
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CB