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eimsori [14]
3 years ago
7

2. MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of

75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
7 0

Answer:

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

X \sim N(75,15)  

Where \mu=75 and \sigma=25

The distribution for the sample mean \bar X is given by:

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

b) \mu represent the true average for the scores of the aptitude test

c) We can calculate the z scores and we got:

z = \frac{70.14-75}{\frac{15}{\sqrt{25}}}= -1.62

z = \frac{82.14-75}{\frac{15}{\sqrt{25}}}= 2.38

And we can calculate the probability with this difference:

P(-1.62

d) We can calculate the z scores and we got:

z = \frac{82.68-75}{\frac{15}{\sqrt{25}}}= 2.56

And we can calculate the probability with this difference:

P(Z

e) We can calculate the z scores and we got:

z = \frac{78.69-75}{\frac{15}{\sqrt{25}}}= 1.23

And we can calculate the probability with this difference:

P(Z

Step-by-step explanation:

a. What are the expected value, the standard deviation, and the shape of the sampling distribution of \bar X?

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 of a population, and for this case we know the distribution for X is given by:

X \sim N(75,15)  

Where \mu=75 and \sigma=25

The distribution for the sample mean \bar X is given by:

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

b. What is the random variable in this problem? Define it in words.

\mu represent the true average for the scores of the aptitude test

c. What is the probability that the average aptitude test score in the sample will be between 70.14 and 82.14?

We can calculate the z scores and we got:

z = \frac{70.14-75}{\frac{15}{\sqrt{25}}}= -1.62

z = \frac{82.14-75}{\frac{15}{\sqrt{25}}}= 2.38

And we can calculate the probability with this difference:

P(-1.62

d. What is the probability that the average aptitude test score in the sample will be greater than 82.68?

We can calculate the z scores and we got:

z = \frac{82.68-75}{\frac{15}{\sqrt{25}}}= 2.56

And we can calculate the probability with this difference:

P(Z

e. What is the probability that the average aptitude test score in the sample will be less than 78.69?

We can calculate the z scores and we got:

z = \frac{78.69-75}{\frac{15}{\sqrt{25}}}= 1.23

And we can calculate the probability with this difference:

P(Z

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Answer:

See explanation below.

Step-by-step explanation:

The equation is:

y = 7x + 6

This is the equation of a line in slope intercept form. The general form, where m is the slope and b is the y intercept is:

y = mx + b

In this case, with the equation:

y = 7x + 6

m is 7 and the y intercept is 6.

The y intercept means the point when x = 0:

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Hope this Helps! Have an Awesome Day!! (-:

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Zolol [24]

1.) The error is that she attached the

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constant (which is variable).

The correct equation is:

365+125x=250+175x

2.) N=5

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2 years ago
If x is a rational number and y is the opposite of x, why do x and y have the same absolute value
grin007 [14]

Answer:

Absolute value is the distance away from zero, so if x is a rational number and y is opposite, they would both be the same distance away from zero, regardless of their sign.  

Step-by-step explanation:

Absolute value is the distance of a number away from zero.  For example, if x is equal to the rational number -2, the absolute value of -2 is just 2, given that both 2 and -2 are only a distance of 2 away from the number zero.  Think of it as your walk or drive to school.  If you live 4 miles from school, you drive a distance of 4 miles there and 4 miles back.  That distance is not calculated as a positive 4 miles there and a negative 4 miles back, but rather just 4 miles there and 4 miles back, for a total distance of 8 miles.  So, if x=4 and y=(-4), the absolute value of both would be 4.  

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6 0
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One number is 16 more than another number. The two numbers have a sum of 120. Wbich system of equations could you use to find th
joja [24]

Step-by-step explanation:

Let, 1st number be x and 2nd number be y

Then,

equation 1

x = 16+y

equation 2

x + y = 120

or, y = 120 - x

now,

x = 16 + y

or, x= 16 + 120 - x (putting the value of y from equation 2 )

or, x + x = 136

or, 2x =136

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Then,

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or, y= 52

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