Question

Asked Mar 5, 2019

1076 views

In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 72 and a standard deviation of 7. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D.

The lowest score that would qualify a student for an A is________ (Round up to the nearest integer as needed.)

The lowest score that would qualify a student for a B is_______ (Round up to the nearest integer as needed.)

The lowest score that would qualify a student for a C is ______ (Round up to the nearest integer as needed.)

The lowest score that would qualifty a student for a D is______ ( Round up to the nearesr integer as needed.)

Step 1

**Finding the lowest score that would qualify a student for an A grade:**

The points for the final exam are normally distributed with mean 72 and a standard deviation of 7. The top 10% (=0.10) of the students received an A grade. Thus, the lowest score that would qualify a student for an A grade is the upper limit of the area under the normal curve to the left of 0.90 (=1–0.10).

That is, to find the lowest score that would qualify a student for an A grade is the *x*-value corresponding to the probability 0.90 is obtained.

**Software Procedure:**

Step by step procedure to find the *x*-value by using MINITAB software is as follows:

- Choose
**Graph > Probability Distribution Plot**>**View Probability****> OK.** - From
**Distribution**, choose ‘**Normal**’ distribution. - Enter
**Mean**as**72**and**Standard deviation**as**7**. - Click the
**Shaded Area** - Choose
**probability**and**Left Tail**for the region of the curve to shade. - Enter the
**probability**as**90**. - Click
**OK**.

Output using MINITAB software is as follows:

Step 2

Thus, the lowest score that would qualify a student for an A grade is **81.**

Step 3

**Finding the lowest score that would qualify a student for a B grade:**

The top 20% (=0.20) of the students received B grade and 10% (=0.10) received A grade. Thus, the lowest score that would qualify a student for a B grade is the upper limit of the area under the normal curve to the left of 0.70 (=1–0.30).

That is, to find the lowest score that would qualify a student for a B grade is the *x*-value corresponding to the probability 0.70 is obtained.

**Software Procedure:**

Step by step procedure to find the *x*-value by using MINITAB software is as follows:

- Choose
**Graph > Probability Distribution Plot**>**View Probability****> OK.** - From
**...**

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: A random sample of 30 binomial trials resulted in 12 success. Test the claim that the population por...

A: Hey, since there is multiple subpart questions posted, we will answer first three subparts. If you w...

Q: A simple random sample of n=23 professors at a local community college have a mean course evaluation...

A: Solution:Null and alternative hypotheses:Null hypothesis: µ = 4Alternative hypothesis: µ ≠ 4Test sta...

Q: Statistics Question

A: According to the provided information, the variable ‘x’ be age of the best actress winner and ‘y’ be...

Q: Five children aged 2, 3, 5, 7 and 8 years old weigh 14, 20, 32, 42 and 44 kilograms respectively. Fi...

A: Let x be the age of children and y be the weight of children.The equation of the regression line is:

Q: Are there ever any circumstances when a correlation such as Pearson's r can be interpreted as eviden...

A: Correlation between any two variables tell us the linear association meaning that one variable rise ...

Q: 10) Two cards are drawn from a standard deck of 52 cards and the first is not replaced before the se...

A: In this question, we have to draw two cards from a deck of 52 cards without replacement. Then we hav...

Q: directions construct a confidence interval of the population proportion at the given level of confid...

A: Confidence interval:It is given that n = 500 and x = 120.The (1−α)% confidence interval for proporti...

Q: In baseball, is there a linear correlation between batting average and home run percentage? Let x re...

A: In this question we have the given data and using which we have to plot the scatter plot, and best l...

Q: Is there a difference in the weights of contents in a can of Diet Coke versus a regular can of Coke?...

A: Solution:Null and alternative hypotheses:Null hypothesis: µ1−µ2 = 0Alternative hypothesis: µ1−µ2 ≠ 0...