The heights of 1000 students are normally distributed with a mean of 174.5 centi

Question

The heights of 1000 students are normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have height
a) equal to 175 centimeters?
b) greater than or equal to 188.0 centimeters?
PLEASE SHOW ALL WORK AS TO HOW YOU ARRIVED AT THE ANSWER IN ADDITION TO HOW YOU FOUND THE PROBABILITY

Explanation / Answer

(a) P(X = 175)= P( z= 175-174.5/6.9) = 0.072 So number of students equal to 175 centimeters =0.072*1000 =72 -------------------------------------------------------------------------------------------- (b) P(X>=188) = P[ z>= (188-174.5)/6.9] = P[z >= 1.95]=1-0.9744 So number of students = (1-0.9744)*1000 = 25.6

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