Question

1. kitchen appliances dont last forever. the lifespan of all microwave ovens sold in the united states is approximately normally distributed with a mean of 9 years and a standard deviation of 2.5 years. what percentage of the ovens last more than 10 years? (a) 11.5% (b) 34.5% (c) 65.5% (d) 69% (e) 84.5%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 10$ (the value we are interested in), $\mu=9$ (the mean), and $\sigma = 2.5$ (the standard deviation). So, $z=\frac{10 - 9}{2.5}=\frac{1}{2.5}=0.4$.

Step2: Find the cumulative probability

We use the standard normal distribution table (or z - table) to find $P(Z\leq0.4)$. Looking up 0.4 in the z - table, we get $P(Z\leq0.4)=0.6554$.

Step3: Find the probability of $Z>0.4$

Since the total area under the normal curve is 1, $P(Z > 0.4)=1 - P(Z\leq0.4)$. So, $P(Z>0.4)=1 - 0.6554 = 0.3446\approx34.5\%$.

Answer:

B. 34.5%