Respuesta :
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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=\text{ z-score}[/tex],
[tex]x=\text{Random sample score}[/tex],
[tex]\mu=\text{ Mean}[/tex],
[tex]\sigma=\text{ Standard deviation}[/tex].
Let us find z-score for random score 660.
[tex]z=\frac{660-715}{24}[/tex]
[tex]z=\frac{-55}{24}[/tex]
[tex]z=-2.29[/tex]
Let us find z-score for random score 680.
[tex]z=\frac{680-715}{24}[/tex]
[tex]z=\frac{-35}{24}[/tex]
[tex]z=-1.458\approx -1.46[/tex]
We will use formula [tex]P(a<z<b)=P(z<b)-P(z<a)[/tex] to find the probability between our given values.
Upon substituting our given values in above formula we will get,
[tex]P(-2.29<z<-1.46)=P(z<-1.45)-P(z<-2.29)[/tex]
Using normal distribution table we will get,
[tex]P(-2.29<z<-1.46)=0.07215-0.01101[/tex]
[tex]P(-2.29<z<-1.46)=0.06114[/tex]
Therefore, the probability that a randomly selected value will be between 660 and 680 is 0.0611 and option B is the correct choice.