Question

The shelf life of a battery produced by a major company is known to be normally distributed, with a mean life of 4 years and a standard deviation of 0.75 years. What is the upper quartile of the battery shelf life? What range of years contains the middle 68% of all battery shelf lives?

Answer 1

4.5 years ; (3.25, 4.75)

Explanation:

Given that :

Mean , m = 4

Standard deviation, s = 0.75

The upper quartile, which is the 3rd quartile of a standard normal distribution is 0.67

Therefore, the upper quartile Q3:

Q3 = mean + 0.67 * standard deviation

Q3 = 4 + 0.67(0.75)

Q3 = 4 + 0.5025

Q3 = 4.5025

Q3 = 4.5 years

Range of values that contain the middle 68%

According to the empirical rule;

68% is within 1 standard deviation of the mean

Therefore ;

Interval will be ;

Mean ± 1 standard deviation

(4 - 0.75) ; (4 + 0.75)

(3.25, 4.75)