Question

1. The number of hours that biology students study per week is normally distributed with a mean of 15 hours and a standard deviation of 5 hours.

a. Draw an approximate picture of the distribution of weekly hours studied for biology students.

b. If a student is chosen at random, what is the probability that the student studies less than 11 hours per week? Include a picture that graphically shows the portion of students that study less than 11 hours per week.

c. If a student is chosen at random, what is the probability that the student studies more than 20 hours per week? Include a picture that graphically shows the portion of students that study more than 20 hours per week.

d. What is the proportion of students that study between 8 and 20 hours per week? Include a picture that graphically shows this.

Answer 1

Let x = The number of hours that biology students study per week

Given that , x is normally distributed with a mean of 15 hours and a standard deviation of 5 hours

i.e. mean

and SD

A ) approximate picture of the distribution of weekly hours studied for biology students is as follows

B ) We want to find the probability that, the student studies less than 11 hours per week

i.e. we want to calculate  

By using Z score we can calculate it

where ,

For x = 11 ,

i.e. we want to calculate  

i.e. we want to calculate

................( From Z table) ...( ANSWER)

The probability that the student studies less than 11 hours per week is 0.2119   ...( ANSWER)

C) we want to find the probability that, the student studies more than 20 hours per week

i.e.

For x = 20 ,   

i.e. we want to calculate the probability that

picture that graphically shows the portion of students that study more than 20 hours per week is as follows

i.e. we want to calculate the probability that

   ...........( From Z table)

..................( ANSWER)

the probability that the student studies more than 20 hours per week is 0.1587 .........( ANSWER)

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D) we want to calculate the proportion of students that study between 8 and 20 hours per week

i.e.

For x = 8 ,   

For x = 20 ,   

i.e. we want to calculate the probability that

............( From table)

.............( ANSWER)

proportion of students that study between 8 and 20 hours per week is 76.06% .........( ANSWER)