Question

A set of data follows a nonstandard normal distribution curve. Find the probability that a randomly selected value will be between 660 and 680 given mean of 715 and a standard deviation of 24
Options:
0.9169
0.0611
0.7100
0.8300

Answer 1

Answer:

0.0611

Step-by-step explanation:

Answer 2

Answer:

B. 0.0611

Step-by-step explanation:

We have been given that a data set which follows a nonstandard normal distribution curve and mean of data set is 715 and standard deviation is 24.

To find the probability that a randomly selected value will be between 660 and 680 we will use probability formula to find the values between two z-scores.

First of all let us find z-score for our given values using z-score formula.

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

$z=\text{ z-score}$,

$x=\text{Random sample score}$,

$\mu=\text{ Mean}$,

$\sigma=\text{ Standard deviation}$.

Let us find z-score for random score 660.

$z=\frac{660-715}{24}$

$z=\frac{-55}{24}$

$z=-2.29$

Let us find z-score for random score 680.

$z=\frac{680-715}{24}$

$z=\frac{-35}{24}$

$z=-1.458\approx -1.46$

We will use formula $P(a<z<b)=P(z<b)-P(z<a)$ to find the probability between our given values.

Upon substituting our given values in above formula we will get,

$P(-2.29<z<-1.46)=P(z<-1.45)-P(z<-2.29)$

Using normal distribution table we will get,

$P(-2.29<z<-1.46)=0.07215-0.01101$

$P(-2.29<z<-1.46)=0.06114$

Therefore, the probability that a randomly selected value will be between 660 and 680 is 0.0611 and option B is the correct choice.