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4 years ago

Find the area to the right of a z score of 2.75 under a standard normal distribution curve.

2 answers:

8 0

The area tom the right of the z-score of 2.75 under a statistical normal distribution curve will be given by:
1-P(z≤2.75)
but
P(z≤2.75)=0.997
thus
1-P(z≤2.75)
=1-0.997
=0.003
Answer: 0.003

zimovet [89]4 years ago

5 0

Answer:

The area to the right of a z score is 0.0030.

A is the correct option.

Step-by-step explanation:

We have been given the z score as 2.75 and we have to find the area to the right of this z score under a standard normal distribution curve.

From the z score table, the area to the left of this z score under a standard normal distribution is given by

$P(z>2.75)=0.9970$

Therefore, in order to find the the area to the right of this z score under a standard normal distribution curve, we can subtract 1 from this the area to the right of this z score under a standard normal distribution curve.

$P(z>2.75)=1-0.9970\\=0.0030$

The area to the right of a z score is 0.0030.

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3 years ago

Candice is preparing for her final exam in Statistics. She knows she needs an 65 out of 100 to earn an A overall in the course.

sertanlavr [38]

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 =

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to of the values.

Therefore, Scores between 72 and 90 =

= 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 =

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

Step-by-step explanation:

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3 years ago

Read 2 more answers