Respuesta :
a)The percentage of students will score below 620 in a typical year is 0.5808.
b)The score that the engineering school should set as a comparable standard on the ACT math test is 24 .
What is Probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Given that;
[tex]\mu=480,\[/tex] [tex]\sigma=100[/tex]
a) The percentage of students who will score below 620 is a typical year is obtained below:Ф
[tex]\therefore P(x < 620)\ =\ P\left(\frac{x-\mu}{\sigma} < \frac{x-480}{100}\right)\\[/tex]
[tex]=\ P\left(\left(z\right) < \frac{620-480}{100}\right)[/tex]
[tex]=\ P\left(\left(z\right) < 1.4\right)[/tex]
[tex]=\ 1-P\left(\left(z\right) > 1.4\right)[/tex]
[tex]=1-0.4192[/tex]
[tex]=0.5808[/tex]
[tex]\therefore[/tex] the percentage of students will score below 620 in a typical year is 0.5808.
b) The average and standard deviation for ACT math score is :
[tex]\mu=18,[/tex] [tex]\sigma=6[/tex]
[tex]\therefore \ P\left(\frac{x-\mu}{\sigma} > \frac{x-18}{6}\right)=1[/tex]
[tex]=\ P\left(\left(z\right) > \frac{x-18}{6}\right)[/tex]
or [tex]\frac{x-18}{6}=1[/tex]
[tex]x =[/tex] 6 x 1 + 18
[tex]x =[/tex] 24
[tex]\therefore[/tex] the score that the engineering school should set as a comparable standard on the ACT math test is 24 .
What is Standard deviation?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
What do you mean by average?
An average is defined as the sum of all the values divided by the total number of values in a given set. It is also known as the arithmetic mean.
Find out more about average and standard deviation:
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