Chapter 3.2, Problem 3.25E

(a)

To determine

To calculate the range of values between them 99.7% of the data falls based on the given data.

Answer to Problem 3.25E

Lower limit = 327

Upper limit = 345

Explanation of Solution

Given:

Mean = 336 days

Standard deviation = 3 days

Concept used:

As per empirical rule

1. 68% of the data falls within one standard deviation from the mean.
2. 95% of the data falls within two standard deviations from the mean.
3. 99.7% of the data falls within three standard deviations from the mean.

Calculation:

  $\begin{array}{c}\text{Lower limit = }\mu \text{- 3}\sigma \\ =336-3\left(3\right)\\ =336-9\\ =327\end{array}$

  $\begin{array}{c}\text{Upper limit = }\mu +\text{3}\sigma \\ =336+3\left(3\right)\\ =336+9\\ =345\end{array}$

(b)

To determine

To calculate the proportion of values that falls beyond that 339 days.

Answer to Problem 3.25E

16% of the data falls beyond the 339 days.

Explanation of Solution

Calculation:

339 is one standard deviation above than the mean therefore the proportion of values that falls beyond 339 is $13.5\%+2.35\%+0.15\%=16\%$ . Therefore, 16% of the data falls beyond the 339.