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.*

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:

Step 3

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

The probability tha...

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