Question

X is a normally distributed random variable with mean 67 and standard deviation 17. What is the probability that X is between 50 and 84?

Answer 1

0.68

Explanation:

Given :

Mean = 67

Standard deviation = 17

Probability that X is between 50 and 84

According to the empirical rule :

1 standard deviation from the mean = 68%

2 standard deviations from the mean = 95%

3 standard deviations from the mean = 99.7%

Evaluating the number of standard deviations from the mean:

50 = 67 - 17 = 1 standard deviation

84 = 67 + 17 = 1 standard deviation

Hence ;

50 < X < 84 is 1 standard deviation from the mean which is 68%

Hence, Probability that x is between 50 and 84 is 0.68