The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable, with a mean of 7.5 hours and a standard deviation of 2.1 hours. Also indicate whether the event is usual or unusual A.  What proportion of A students study more than 10 hours per week B.  Find the probability that an A student spends between 7 and 9 hours studying C.  What proportion of A students spend fewer than 3 hours studying *Please do not solve using Microsoft Excel.  My professor is not teaching using excel.  I would like to see the steps involved to solving the problem for my own study reference for exams.*

Question
Asked Nov 9, 2019

The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable, with a mean of 7.5 hours and a standard deviation of 2.1 hours. Also indicate whether the event is usual or unusual

 

A.  What proportion of A students study more than 10 hours per week 

B.  Find the probability that an A student spends between 7 and 9 hours studying 

C.  What proportion of A students spend fewer than 3 hours studying

 

*Please do not solve using Microsoft Excel.  My professor is not teaching using excel.  I would like to see the steps involved to solving the problem for my own study reference for exams.*

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Expert Answer

Step 1

Introduction:

Consider X as a normally distributed random variable, with mean μ and standard deviation σ. Then, the z-score for a particular value X = x, is:

z = (x μ)/σ.

Step 2

a.Finding the proportion of students who study more than 10 hours per week:

Here, the distribution of amount of time devoted for study follows a normal distribution with mean 7.5 hours and standard deviation 2.1 hours.

Then, the proportion of students who study more than 10 hours per week is obtained as follows:

P(X 10) 1-P(x <10)
1-H*z2,012)
X-u10 -7.5
2.1
-1-P(zs1.19)
Using the standard nomal table,
'P(z 1.19) 0.8830
=1-0.8830
=0.1170
Thus, the proportion of students who study more than 10 hours per week is approximately 12 out
of 100 students
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P(X 10) 1-P(x <10) 1-H*z2,012) X-u10 -7.5 2.1 -1-P(zs1.19) Using the standard nomal table, 'P(z 1.19) 0.8830 =1-0.8830 =0.1170 Thus, the proportion of students who study more than 10 hours per week is approximately 12 out of 100 students

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Step 3

b.Computing the probability that a student spends between 7 and 9 hours studying:

The probability tha...

Р(7<X <9)- Р(x <9)-Р(х <7)
X - и 9-7.5
= P
X—и 7-7.5
- P
2.1
2.1
=P(z 0.71)-P(zs-0.24)
U sing the standard nomal table,
'P(z0.71) 0.7611 and P(z -0.24) 0.4052
0.7611-0.4052
=0.3560
Thus, the probability that a student spends between 7 and 9 hours studying is 0.3560.
help_outline

Image Transcriptionclose

Р(7<X <9)- Р(x <9)-Р(х <7) X - и 9-7.5 = P X—и 7-7.5 - P 2.1 2.1 =P(z 0.71)-P(zs-0.24) U sing the standard nomal table, 'P(z0.71) 0.7611 and P(z -0.24) 0.4052 0.7611-0.4052 =0.3560 Thus, the probability that a student spends between 7 and 9 hours studying is 0.3560.

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