Question

the following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones: suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. how likely is it that a randomly chosen battery lasts longer than 10.4 hours? a. 0.50 b. 0.16 c. 0.05 d. 0.025

Explanation:

Step1: Calculate z - score

$z=\frac{x-\mu}{\sigma}=\frac{10.4 - 8}{1.2}=\frac{2.4}{1.2}=2$

Step2: Find probability

$P(X>10.4)=P(Z > 2)=1 - P(Z\leq2)$
From standard - normal table, $P(Z\leq2)=0.9772$, so $P(Z > 2)=1 - 0.9772 = 0.0228\approx0.025$

Answer:

D. 0.025