standard deviation

Question

Suppose a normal distribution has a mean of 62 and a standard deviation of

4. What is the probability that a data value is between 56 and 64? Round your

answer to the nearest tenth of a percent.

O A. 64.5%

B. 62.5%

O C. 61.5%

D. 63.5%

Answer 1

if x = data value

we want to find P(56 < x < 64) when x is N(62,4) - mean 62, standard deviation (SD) 4

we use z-statistic = (x - mean)/SD to transform x to standard normal distribution: N(0,1)

P(56 < x < 64) = P( (56-62)/4 < z < (64 - 62)/4)

= P(-1.5 < z < 0.5)

= P(z < 0.5) - P(z) < -1.5)

= 0.6915 - 0.0668 = 0.6247 = 62.47% ~ 62.5% (B)