Question

PLEASE HELP!! I WILL BRAINLIEST
A particular data set can be approximately described as a normal distribution.

The mean of the data set is 40 and one standard deviation is 5. About what percent of the numbers fall between 35 and 50?
A.) 53.2%
B.) 68.2%
C.) 77.4%
D.) 81.8%

Answer 1

Answer:

81.8%

Step-by-step explanation:

Mean = $\mu = 40$

Standard deviation = $\sigma = 5$

Now we are supposed to find out what percent of the numbers fall between 35 and 50

$z = \frac{x-\mu}{\sigma}$

Substitute the values

$z = \frac{x-40}{5}$

Now for P(35<x<50)

Substitute x = 35

$z = \frac{35-40}{5}$

$z =-1$

Substitute x = 50

$z = \frac{50-40}{5}$

$z =2$

So, P(-1<z<2)

P(z<2)-P(z<-1)

=0.9772-0.1587

=0.8185

= $0.818 \times 100$

=81.8%

Hence  81.8% percent of the numbers fall between 35 and 50