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A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. Teh mean is 73, wit

zavuch27 [327]

Answer:

The bottom for an A is 75. Round to the nearest whole number as needed.

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the scores on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=73,\sigma=7)$

And let $\bar X$ represent the sample mean, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

2) The bottom for an A is _____. Round to the nearest whole number as needed.

And we want the top 5.5% of the scores, so we need a value a such that:

$P(X>a)=0.055$ or $P(X$

We need on the right tail of the distribution a value a that gives to us 94.5% of the area below and 5.5% of the area above. Both conditions are equivalent.

Let's use the condition $P(X$ , the best way to solve this problem is using the z score with the following formula:

$z=\frac{x-\mu}{\sigma}$

So we need a value from the normal standard distribution that accumulates 0.945 of the area on the left and 0.055 on the right. This value on this case is 1.598 and we can founded with the following code in excel:

"=NORM.INV(0.945,0,1)"

If we apply the z score formula to our case we have this:

$P(X$

So then based on the equalities we have this:

$\frac{a-73}{7}=1.598$

And if we solve for a we got:

$a=(7*1.598) +73=84.186$

So then we need a score of 84.186 rounded to the nearest whole number 75 or higher in order to get an A

8 0

3 years ago

MR MARK MARKS HIS CLASS ON A NORMAL CURVE. THOSE WITH z-SCORES ABOVE 1.8 WILL RECEIVE AN A, THOSE

lukranit [14]

Using the normal distribution, it is found that the percentages are given as follows:

3.59% of the grades will be A.

9.98% of the grades will be B.

74.92% of the grades will be C.

8.64% of the grades will be D.

2.87% of the grades will be F.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The prorportion of students who receive an A is one subtracted by the p-value of Z = 1.8.

Looking at the z-table, Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359.

3.59% of the grades will be A.

For B, it is the p-value of Z = 1.8 subtracted by the p-value of Z = 1.1, hence:

0.9641 - 0.8643 = 0.0998.

9.98% of the grades will be B.

For C, it is the p-value of Z = 1.1 subtracted by the p-value of Z = -1.2, hence:

0.8643 - 0.1151 = 0.7492.

74.92% of the grades will be C.

For D, it is the p-value of Z = -1.2 subtracted by the p-value of Z = -1.9, hence:

0.1151 - 0.0287 = 0.0864.

8.64% of the grades will be D.

For F, it is the p-value of Z = -1.9, hence 2.87% of the grades will be F.

More can be learned about the normal distribution at brainly.com/question/15181104

#SPJ1

7 0

1 year ago

A dolphin swims 665,280 feet in 3 hours. Use the formula dart, where d represents distance, r represents rate, and t represents

barxatty [35]

Step-by-step explanation:

a) r=d/t ( same as formula of speed)

b) r= 665280/3=221760 feet/hr

c) distance in miles = 665280/5280= 126

so r=126/3 = 42 miles/hr

d) i think using miles makes more sense cz using feet will result in greater number of values so there is a greater chance of human error

5 0

3 years ago

Read 2 more answers

I need help plz and thank you this is due

Varvara68 [4.7K]

? What do u need help with? I would be glad to help but there isn’t enough explanation!

5 0

3 years ago

Read 2 more answers

Please answer correctly thank you!

Nina [5.8K]

If you rotate the triangle so that the 6 is on the bottom, the two sides are both 6.2.

Because the two sides are equal the two angles at the bottom would also be equal. One is given as 61 degrees, so the other bottom angle is also 61 degrees.

The three inside angles of a triangle need to equal 180, so X would equal 180 minus the two bottom angles.

X = 180 - 61 - 61 = 58 degrees.

5 0

3 years ago