Question

Suppose a normal distribution has a mean of 222 and a standard deviation of 16. What is the probability that a data value is between 174 and 238? Round your answer to the nearest tenth of a percent.

A. 66.9%
B. 53.3%
C. 84.0%
D. 91.0%

Answer 1

P(174 < x < 238) = P(x < 238) - P(x < 174) = P[z < (238 - 222)/16] - P[z < (174 - 222)/16] = P(z < 1) - P(z < -3) = 0.84134 - 0.00135 = 0.83999 or 83.999%

Answer: 84.0% to the nearest tenth.