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emmainna [20.7K]
3 years ago
6

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Befor

e the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $400 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's .
Find the point in the distribution below which 2.5% of the PCE's fell.



a. $302



b. $10



c. $390



d. $498
Mathematics
1 answer:
Zolol [24]3 years ago
4 0

Answer:

a. $302

Step-by-step explanation:

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.

In this question, we have that:

\mu = 400, \sigma = 50

Point in the distribution below which 2.5% of the PCE's fell.

This is the 2.5th percentile, which is X when Z has a pvalue of 0.025. So it is X when Z = -1.96.

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

-1.96 = \frac{X - 400}{50}

X - 400 = -1.96*50

X = -1.96*50 + 400

X = 302

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andre [41]

Answer:

Inverse of the function does not exist.

Step-by-step explanation:

Inverse of a function: Inverse of a function f(x) is a function that brings range to domain of f(x).

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This function is not one-one map because f(x)=f(-x)

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Hence here inverse function does not exist.

3 0
4 years ago
Express this number in scientific notation.
Nady [450]

Answer:

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Step-by-step explanation:

Move the decimal until it is between the first and second number

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7 0
4 years ago
Read 2 more answers
I need help in find the value of the variables please!!!!
lord [1]

Answer:

11: x=90 and y=10

12:  x=59 and y=48

14?: x = 28,   y = 20 and z = 56

15:  x = 4 and y = 53

Step-by-step explanation:

11:  Since two sides are parallel, you can draw a transversal (a line that crosses through both) that makes sure all angles it makes are 90 degrees.  (let me know if that doesn't make sense.  Now you have two trapezoids.  One has angle measures 90+90+90+x=360 and the other has 90+90+77+y = 360.  Doing some quick algebra gets you x=90 and y=10

12:  We do the same thing, transversal throught he parallel lines to get four  90 degree angles.  Now 360 = 90 + 90 + 2x + 62 makes x = 59 and 360 = 90 + 90 +3 y + 42 makes y = 48

(14?  the one to the left of 15):  Could do the same thing to solve for x, then we need to do something different for y and z.  so first 90 + 90 + 68 + 4x = 360 so x=28.  Now, since this is an isosceles trapezoid it means the two top angles are equal and the two bottom angles are equal.  so 68 =3y+8 so y = 20 and 2z = 4x = 4(28)  makes z = 56

for 15 we'll start with y.  We will call the two equal angles a, because we need to use them.  Since the top and bottom  parts are parallel, 106 + a = 180 and 2y + a = 180.  Use a system of equations to find a = 74 and y = 53 (You just needed y of course).  since 2y=106, we know that 4x=6x-8 so then we can solve for x = 4

5 0
4 years ago
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lakkis [162]

C(2.4) does not represent this ratio.

8 0
3 years ago
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Can someone please help
boyakko [2]
The answer is it is a statistic because the value describes a characteristic of a sample.
3 0
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