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joja [24]
3 years ago
10

PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!

Mathematics
1 answer:
Contact [7]3 years ago
6 0
Which one to do cuz it’s confused
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Time spent using​ e-mail per session is normally​ distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that
liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 11, \sigma = 3

a. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 10.8 and 11.2 ​minutes?

Here we have that n = 25, s = \frac{3}{\sqrt{25}} = 0.6

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{11.2 - 11}{0.6}

Z = 0.33

Z = 0.33 has a pvalue of 0.6293.

X = 10.8

Z = \frac{X - \mu}{s}

Z = \frac{10.8 - 11}{0.6}

Z = -0.33

Z = -0.33 has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 ​sessions, what is the probability that the sample mean is between 10.5 and 11 ​minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

Z = \frac{X - \mu}{s}

Z = \frac{11 - 11}{0.6}

Z = 0

Z = 0 has a pvalue of 0.5.

X = 10.5

Z = \frac{X - \mu}{s}

Z = \frac{10.5 - 11}{0.6}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 ​sessions, what is the probability that the sample mean is between 10.8 and 11.2 ​minutes?

Here we have that n = 100, s = \frac{3}{\sqrt{100}} = 0.3

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{11.2 - 11}{0.3}

Z = 0.67

Z = 0.67 has a pvalue of 0.7486.

X = 10.8

Z = \frac{X - \mu}{s}

Z = \frac{10.8 - 11}{0.3}

Z = -0.67

Z = -0.67 has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0
3 years ago
Solve for g 3g-10=-45​
Goryan [66]

Answer:

g = -18.3

Step-by-step explanation:

3g-10=-45

+10 (Cancel out the 10)

3g=-55

/3 (Divide by 3 to cancel out the 3)

g= -18.3

5 0
3 years ago
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How is the graph of y = 7x2 + 4 different from the graph of y = 7x2?
Karolina [17]
It shifted 4 u it’s to the left
6 0
3 years ago
The perimeter of a triangle is 42 yards. the first side is 5 yards less than the second side, and the third side is 2 yards less
Zina [86]
The 1st side is 13 yards, the 2nd is 18 yards, and the 3rd is 11 yards
7 0
3 years ago
Read 2 more answers
A number cube with the numbers 1 through 6 is rolled.
olchik [2.2K]

Answer:

Step-by-step explanation:

Given that, we have a number cube label 1,2,3,4,5 and 6.

Then, the sample space is

S= {1, 2, 3, 4, 5, 6}

The probability of rolling a number different from 9?

Since we don't have 9 in the sample space, then the probability of rolling a number different from 9 will be the have 1,2,3,4,5 and 6 as the outcome

Then,

Pr(rolling number different from 9) = 6 / 6 = 1

Pr(rolling number different from 9) = 1.

The second option is correct.

6 0
3 years ago
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