Question

Given a normal distribution with u = 100 and o = 10, complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table. B Click here to view page 2 of the cumulative standardized normal distribution table. a. wnat is the probability tnat x>85? The probability that X> 85 is ]. (Round to four decimal places as needed.) b. What is the probability that X < 75? The probability that X< 75 is . (Round to four decimal places as needed.) c. What is the probability that X<70 or X> 110? The probability that X < 70 or X> 110 is . (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (symmetrically distributed around the mean)? 99% of the values are areater than and less than I.

Answer 1

a) X (100,10) implies Z=(X-100)/10 N(0,1) P(X>85)=1-(-1.5) = (1.5) = 0.9332 b) P(X<75)=(-2.5) = 0.0062 c) P(X<70 or X>110)=P(X<70) +P(X>110)=(-3) +1 -0(1) = 2 - (1)-°(3) = 1600 d) Let the upper value be A. Then due to symmetry, A must be such that P(X>A)=.005 or P = T.005 = 2.57583 or A=125.7583 Then the lower value is 100-(125.7583-100)=74.2417 (as these values are symmetrically placed around mean) 99% of the values are greater than 74.2417 and less than 125.7583

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