Chapter 6, Problem 48E

a)

To determine

To find the standard deviation.

Answer to Problem 48E

The standard deviation is 3.2520

Explanation of Solution

Given:

  $\mu$ = 74

  $x$ =70

Formula:

  $z=\frac{x-\mu }{\sigma }$

First, we need to find z-score corresponding to a probability of 11%.

  P(Z< z) = 0.11

  z = -1.23

Using formula,

  $\begin{array}{l}-1.23=\frac{70-74}{\sigma }\\ \sigma =3.2520\end{array}$

b)

To determine

To find the mean.

Answer to Problem 48E

The mean is 75.691

Explanation of Solution

Given:

  $x$ =70

  $\sigma =3.2520$

Formula:

  $z=\frac{x-\mu }{\sigma }$

First, we need to find z-score corresponding to a probability of 4%.

  P(Z< z) = 0.04

  z = -1.75

Using formula,

  $\begin{array}{l}-1.75=\frac{70-\mu }{3.2520}\\ \mu =75.691\end{array}$

Hence, the mean is 75.691

c)

To determine

To find the standard deviation of new variety.

Answer to Problem 48E

The standard deviation is 2.8571.

Explanation of Solution

Given:

  $\mu$ = 74

  $x$ =70

Formula:

  $z=\frac{x-\mu }{\sigma }$

First, we need to find z-score corresponding to a probability of 4%.

  P(Z< z) = 0.04

  z = -1.75

Using formula,

  $\begin{array}{l}-1.75=\frac{70-75}{\sigma }\\ \sigma =2.8571\end{array}$

Hence, the standard deviation is 2.8571.

d)

To determine

To compare old and new variety.

Answer to Problem 48E

The new variety of Romas are more consistent in their weights.

Explanation of Solution

Given:

The standard deviation of old variety is 3.2520

The standard deviation of new variety is 2.8571.

If the standard deviation is smaller then the values are said to be more consistent. Hence, the new variety of Romas are more consistent in their weights.