4. kitchen appliances dont last forever. the lifespan of all microwave ovens sold in the united states is…

4. 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%

4. 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%

Answer

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%