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Salsk061 [2.6K]

2 years ago

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Harlamova29_29 [7]2 years ago

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The amount of time all students in a very large undergraduate statistics course take to complete an examination is distributed c

Anestetic [448]

Answer:

a) The mean is $\mu = 60$

b) The standard deviation is $\sigma = 9$

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The probability a student selected at random takes at least 55.50 minutes to complete the examination equals 0.6915.

This means that when X = 55.5, Z has a pvalue of 1 - 0.6915 = 0.3085. This means that when $X = 55.5, Z = -0.5$

So

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

$-0.5 = \frac{55.5 - \mu}{\sigma}$

$-0.5\sigma = 55.5 - \mu$

$\mu = 55.5 + 0.5\sigma$

The probability a student selected at random takes no more than 71.52 minutes to complete the examination equals 0.8997.

This means that when X = 71.52, Z has a pvalue of 0.8997. This means that when $X = 71.52, Z = 1.28$

So

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

$1.28 = \frac{71.52 - \mu}{\sigma}$

$1.28\sigma = 71.52 - \mu$

$\mu = 71.52 - 1.28\sigma$

Since we also have that $\mu = 55.5 + 0.5\sigma$

$55.5 + 0.5\sigma = 71.52 - 1.28\sigma$

$1.78\sigma = 71.52 - 55.5$

$\sigma = \frac{(71.52 - 55.5)}{1.78}$

$\sigma = 9$

$\mu = 55.5 + 0.5\sigma = 55.5 + 0.5*9 = 55.5 + 4.5 = 60$

Question

The mean is $\mu = 60$

The standard deviation is $\sigma = 9$

6 0

2 years ago

An internet search engine looks for a keyword in 9 databases, searching them in a random

atroni [7]

Here you go! I hope I can get brainliest!

8 0

2 years ago

Write and expression for “the sum of d and 9”

Natali [406]

Sum means to Add.

So the sum of d and 9 would be d + 9

5 0

2 years ago

Read 2 more answers

cestrela7 [59]

Answer:

-1

Step-by-step explanation:

You have to use simultaneous linear equation as there are 2 equations given

use the subtitution method as what I've shown above

Hope you can understand well

Stay safe!

4 0

2 years ago

Read 2 more answers

NEED ANSWER ASAP!!!! <br> y=−x^2−2x+3 <br> When is g(x) = 0?

Crazy boy [7]

Answer:

$y=3$

Step-by-step explanation:

Since g(x)=0, you input 0 into every x

$y=-(0)^{2} -2(0)+3$

Which then becomes:

$y=0+3$

Take out the 0 and there's your answer

7 0

2 years ago