91影视

Referring to exercise 2.23, in sustainability behaviors of CPA corporations, the level of support for corporate sustainability was obtained by 992 senior managers at CPA firms.

The level of support for sustainability x has a mean of 67.755 and a standard deviation of 26.871

Assume that x is normally distributed.

Here the mean and standard deviation of the random variable x is given by,

$$\begin{gathered} 渭=67.755and蟽=26.871 \\ x=40 \end{gathered}$$

The z-score is,

$$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{40-67.755}{26.871} \\ =-1.0329 \\ P(x<40)=P(x<40) \\ =P(z<1.0329)) \\ =1-0.8485 \\ =0.1515 \\ P(x<40)=0.1515 \end{gathered}$$

Thus, the required probability is 0.1515.

Here the mean and standard deviation of the random variable x is given by,

$$\begin{gathered} 渭=67.755and蟽=26.871 \\ x=40 \end{gathered}$$

The z-score is,

$$\begin{gathered} =\frac{40-67.755}{26.871} \\ =-1.0329 \end{gathered}$$

Again,

$$\begin{gathered} x=120 \\ z=\frac{x-渭}{蟽} \\ =\frac{120-67.755}{26.871} \\ =1.9443 \\ P(40<x<120)=P(x<120)-P(x<40) \\ =P(z<1.9443)-P(z<1.0329) \\ =P(z<1.9443)-(1-P(z<1.0329\left)\right) \\ =0.9738-1+0.8485 \\ =0.8223 \end{gathered}$$

Thus, the required probability is 0.8223.

Here the mean and standard deviation of the random variable x is given by,

$$\begin{gathered} 渭=67.755and蟽=26.871 \\ x=120 \\ z=\frac{x-渭}{蟽} \\ =\frac{120-67.755}{26.871} \\ =1.9443 \\ P(x>120)=(1-P(x<120\left)\right) \\ =(1-P(z<1.9443\left)\right) \\ =1-0.9738 \\ =0.0262 \\ P(x>120)=0.0262 \end{gathered}$$

Thus, the required probability is 0.0262.

Let a be the support vale,

$$\begin{gathered} Px<a)=\frac{1}{4} \\ P\left(\frac{x-渭}{蟽}<\frac{x-渭}{蟽}\right)=0.25 \\ P\left(z<\frac{a-67.755}{26.871}\right)=0.25 \\ 桅\left(\frac{a-67.755}{26.871}\right)=0.25 \\ \frac{a-67.755}{26.871}={桅}^{-1}(0.25) \\ a=67.755+26.871脳{桅}^{-1}(0.25) \\ a=67.755+26.871脳(-0.67449) \\ a=49.63077921 \\ a=49.6 \\ a=49.6 \end{gathered}$$

So, the value of a is 49.6

Therefore, one-fourth of the 992 senior managers with corporate sustainability below is 49.6.