Question

initial knowledge check question 15 the batteries from a certain manufacturer have a mean lifetime of 860 hours, with a standard deviation of 70 hours. assuming that the lifetimes are normally distributed, complete the following statements. (a) approximately? of the batteries have lifetimes between 720 hours and 1000 hours. 68% 75% (b) approximately hours batteries have lifetimes between hours and 95% 99.7%

Explanation:

Step1: Calculate z-scores for part (a)

For 720 hours: $z_1 = \frac{720 - 860}{70} = -2$
For 1000 hours: $z_2 = \frac{1000 - 860}{70} = 2$

Step2: Match z-scores to empirical rule

Values within $z=\pm2$ cover 95% of data.

Step3: Use empirical rule for part (b)

99.7% of data lies within $z=\pm3$.
Lower bound: $860 - 3\times70 = 650$
Upper bound: $860 + 3\times70 = 1070$

Answer:

(a) 95%
(b) 650 hours and 1070 hours