Question

1. the hold time experienced by people calling a government agency was found to be normally distributed with a mean of 12.4 minutes and a standard deviation of 4.3 minutes. what percent of calls are answered in less than 5 minutes? round to the nearest tenth.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 5$ (the value we are interested in), $\mu=12.4$ (the mean) and $\sigma = 4.3$ (the standard deviation).
Substitute the values into the formula: $z=\frac{5 - 12.4}{4.3}=\frac{- 7.4}{4.3}\approx - 1.72$

Step2: Find the area to the left of the z - score

We need to find $P(Z < - 1.72)$ using the standard normal distribution table (or a calculator with a normal - distribution function).
Looking up $z=-1.72$ in the standard normal table, the area to the left of $z = - 1.72$ is approximately $0.0427$.

Step3: Convert the proportion to a percentage

To convert the proportion $0.0427$ to a percentage, we multiply by 100: $0.0427\times100 = 4.27\%$

Step4: Round to the nearest tenth

Rounding $4.27\%$ to the nearest tenth gives $4.3\%$

Answer:

$4.3\%$