Question

the following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones: select one answer 10 points 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 the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 10.4$, $\mu=8$, and $\sigma = 1.2$.
$z=\frac{10.4 - 8}{1.2}=\frac{2.4}{1.2}=2$

Step2: Find the probability

We want to find $P(X>10.4)$, which is equivalent to $P(Z > 2)$ in the standard normal distribution. Since the total area under the standard - normal curve is 1, and $P(Z\leq z)+P(Z > z)=1$, and from the standard normal table $P(Z\leq2)=0.9772$. So $P(Z > 2)=1 - 0.9772=0.0228\approx0.025$.

Answer:

D. 0.025