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Kaylis [27]
3 years ago
14

True or False: The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes a

nd a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.
Mathematics
1 answer:
nekit [7.7K]3 years ago
6 0

Answer:

True

Step-by-step explanation:

To solve this question, we need to understand 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, the sample means with size n of at least 30 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 = 65, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1

If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

This probability is 1 subtracted by the pvalue of Z when X = 71. So

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

By the Central Limit Theorem

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

Z = \frac{71 - 65}{1}

Z = 6

Z = 6 has a pvalue very close to 1.

1 - 1 = 0.

So approximately 0 probability that the sample mean of the sampled students exceeds 71 minutes.

The answer is true.

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3 years ago
Whats the answer plz?10 points!:)
jeyben [28]

Answer:


Step-by-step explanation:

f(x) = 3x + 1 and g(x) = x^2 - 6

(f + g) (x)

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I hope this helps!


7 0
3 years ago
F(x)=9÷4x-15 for x=4
enyata [817]

9/4x  -15     for x=4

To find this answer you must plug the 4 everywhere the x is located.

(9/4)(4)  -15

Multiply 9/4 by 4

(9/4) x 4 = 9

Now we take our 9 answer and add it to -15.

9-15 = -6

The answer is -6

-

-

For the other equation, you also must plug in 3 where ever x is located in the equation.

5/3x -3/5

(5/3)(3) -3/5

Multiply 5/3 and 3

(5/3) x 3 = 5

Take that answer of 5 and add -3/5

5- (3/5) =4 2/5

The answer to this equation would be 4 2/5 or 4.4

5 0
3 years ago
15<br>a) 5<br>5 +<br>8<br>27<br>of 1<br>+<br>99<br>5​
velikii [3]

Answer:

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Step-by-step explanation:

Add the expressions.

7 0
3 years ago
Some friends plotted the locations of their house on a map. brianna's house is at (1,6), Jordan's house is at (5,3). What is one
Rufina [12.5K]
Let
A (1,6)------> location <span>brianna's house on a map
B </span>(5,3)------> location Jordan's house on a map

we know that
One possible path from brianna's house to jordan's house it's a straight line  ( <span>the shortest distance)</span>

using a graph tool
see the attached figure

find the distance points AB
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(3-6)²+(5-1)²]----> d=√[3²+4²]
d=√25----> d=25 units

the distance from brianna's house to jordan's house is 25 units

4 0
3 years ago
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