Question

1. For a standard normal distribution, given:

P(z < c) = 0.7232

Find c. (WHERE is this on the z score table and can I figure in excel/sheets?)

2. For a standard normal distribution, find:

P(z > c) = 0.0912

Find c.

3. About___ % of the area under the curve of the standard normal distribution is between z=−2.837z=-2.837 and z=2.837z=2.837 (or within 2.837 standard deviations of the mean). (HOW- preferably through technology/excel/sheets)

4. About___ % of the area under the curve of the standard normal distribution is outside the interval z=[−0.71,0.71]z=[-0.71,0.71] (or beyond 0.71 standard deviations of the mean).

5. Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z=−1.5z=-1.5 and z=1.5z=1.5standard deviations of the mean (or within 1.5 standard deviations of the mean). What percent of the data points will fall in that range?

Answer:___ percent (Enter a number between 0 and 100, not 0 and 1 and round to 2 decimal places)

Thank you for explaining how and using current technology/quickest way (avpid tables and formulas if possibly) Thanks a million!!

Answer 1

Solution :

Using standard normal table,

1)

P(z < c) = 0.7232

To see the probability 0.7232 in the standard normal table the cumulative z value is 0.59 .

P(z < 0.59) = 0.7232

c = 0.59

2)

P(z > c) = 0.0912

1 - P(z < c) = 0.0912

P(z < c) = 1 - 0.0912 = 0.9088

P(z < 1.33) = 0.9088

c = 1.33

3)

P(-2.837 < z < 2.837) = P(z < 2.837 ) - P(z < -2.837) = 0.9977 - 0.0023 = 0.9954

About 99.54% of the area under the curve of the standard normal distribution is between