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emmainna [20.7K]
2 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]2 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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The atmospheric pressure at sea level is 14.7 lb/in2. This pressure is reduced by half for each 3.6 miles above sea level. Which
Korvikt [17]

<u>Solution-</u>

The atmospheric pressure at sea level = 14.7 lb/in²

Pressure gets reduced by half for each 3.6 miles we move up.

Taking,

x = miles above the sea-level

y = pressure in lb/in²

0         14.7

3.6         7.35

7.2         3.675

10.8         1.8375

It can be observed that both the variables are in inverse proportion as the distance from sea-level increase the pressure decreases.

As only the second graph satisfies the points and inverse proportional condition, so that is the correct graph.

By plotting the graph in excel taking these data set, the following plot was obtained.

8 0
2 years ago
Read 2 more answers
In a study in Scotland (as reported by Devlin 2009), researchers left a total of 320 wallets around Edinburgh, as though the wal
Ann [662]

Answer:

a) The observed proportion of wallets that were returned

  p = 0.45625

b) <em> 95% of confidence intervals for Population proportion</em>

<em>  0.40168  , 0.51082)</em>

<em>c) The lower bound of the 95% confidence interval = 0.40168</em>

<em>d) The upper bound of the 95% confidence interval = 0.51082</em>

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

a)

Given data the  researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them

Given sample size 'n' = 320

  Given data          'x ' = 146

<em>Sample proportion </em>

              p = \frac{x}{n}

             p = \frac{x}{n} = \frac{146}{320} = 0.45625

<u><em>Step(ii)</em></u>:-

b)<em> </em><u><em>95% of confidence intervals for Population proportion</em></u>

Level of significance = 95% or 0.05%

Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96

<em>95% of confidence intervals for Population proportion are determined by</em>

<em></em>(p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })<em></em>

<em></em>(0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })<em></em>

<em>(0.45625 - 0.05457 , 0.45625 + 0.05457)</em>

<em>(   0.40168  , 0.51082) </em>

<em>c) The lower bound of the 95% confidence interval = 0.40168</em>

<em>d) The upper bound of the 95% confidence interval = 0.51082</em>

7 0
1 year ago
2 groups of 10 tiles and 2 groups of 3 tiles. Which explains whether or not this model accurately shows 26 ÷ 2? It does because
WINSTONCH [101]

Answer:

It does because 26 = 20 + 6, and the model shows 2 groups of 10 and 2 groups of 3.  

Step-by-step explanation:

Two groups of 10 make 20. Two groups of 3 make 6.

20 + 6 = 26

B is wrong. The model does not show two groups of 6.

C is wrong. The model should show one group of 6..

D is wrong. The model should show two groups of 10 and one group of 6.

7 0
2 years ago
A little girl is watching planes take off of the runway from a building's rooftop 40 meters away from the airport. If the height
worty [1.4K]

Answer:

h = 417.81 meters

The altitude of the plane is 417.81 meters

Step-by-step explanation:

given;

The initial height of the girl h0 = 400 m

Horizontal distance from the airport d = 40 m

Angle of elevation of the plane ∅= 24°

The altitude of the plane when the picture was taken is equal to initial height of the girl plus the elevation height.

h = he + h0

And he (elevation height) can be derived as;

he = dtan∅

he = 40tan24°

Substituting into the equation;

h = 40tan24° + 400

h = 417.81 meters

The altitude of the plane is 417.81 meters

5 0
1 year ago
One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the tea
andrew11 [14]

Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are given the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean of score change

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{23}{12} = 1.92

b) standard deviation for this population

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences = 126.92

\sigma = \sqrt{\frac{126.92}{12}} = 3.25

c) median change score

Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median =

\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5

d) change score that is 2.2 standard deviations below the mean.

x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23

4 0
1 year ago
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