The mean of a normal probability distribution is 60; thestandard deviation is 5.

Question

The mean of a normal probability distribution is 60; thestandard deviation is 5. A. About what percent of the observations lie between 55& 65? B. About what percent of the observations lie between 50and 70? C. About what percent of the observations lie between 45& 75? The mean of a normal probability distribution is 60; thestandard deviation is 5. A. About what percent of the observations lie between 55& 65? B. About what percent of the observations lie between 50and 70? C. About what percent of the observations lie between 45& 75?

Explanation / Answer

. 1.   To convert from the normal distribution to thestandard normal distribution: z = (x-)/ 2.   z = (x-60)/(5) . 3.   Part A: 4.   z = (55-60)/(5) = -1.00 5.   z = (65-60)/(5) = +1.00 6.   from the standard normal tables:   1.00corresponds to 0.3413 7.   % between 55 and 65 = (100%)*P[-1.00 z 1.00] = (100%)*(2)*(0.3413) =68.26% . 8.   Part B: 9.   z = (50-60)/(5) = -2.00 10.   z = (70-60)/(5) = +2.00 11.   from the standard normal tables:   2.00corresponds to 0.4772 12.   % between 50 and 70 = (100%)*P[-2.00 z 2.00] = (100%)*(2)*(0.4772) =95.44% . 13.   Part C: 14.   z = (45-60)/(5) = -3.00 15.   z = (75-60)/(5) = +3.00 16.   from the standard normal tables:   3.00corresponds to 0.4987 17.   % between 45 and 75 = (100%)*P[-3.00 z 3.00] = (100%)*(2)*(0.4772) =99.74% .

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