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ivolga24 [154]
3 years ago
13

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets retu

rned. A Houston department store sampled 80 items sold in January and found that 8 of the items were returned. (a) Construct a point estimate of the proportion of items returned for the population ofsales transactions at the Houston store. If required, round your answer to three decimal places.
Mathematics
1 answer:
KatRina [158]3 years ago
8 0

Answer:  0.1

Step-by-step explanation:

Given :  A Houston department store sampled 80 items sold in January and found that 8 of the items were returned.

In other words, sample size : <em>n</em>=1040

Number of items returned : <em>x</em>= 8

Let <em>p</em> be the proportion of items returned for the population of sales transactions at the Houston store.

As per sample , the sample proportion of items returned for the population of sales transactions at the Houston store is :

\hat{p}=\dfrac{x}{n}=\dfrac{8}{80}=0.1

As we know that , <em>the sample proportion is the best estimate of the population proportion.</em>

Therefore,a point estimate of the proportion of items returned for the population of sales transactions at the Houston store is 0.1.

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Scores on a final exam taken by 1200 students have a bell shaped distribution with mean=72 and standard deviation=9
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Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean $ \pm $ Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 = $ \frac{68}{100} \times 1200 $

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean $ \pm $ 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to $ \frac{95}{2} \% $ of the values.

Therefore, Scores between 72 and 90 = $ \frac{95}{2(100)} \times 1200 = \frac{95}{200} \times 1200  $

$ \implies 95 \times 12 $ = 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 = $ \frac{2.5}{100} \times 1200 $

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8 0
2 years ago
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Anna007 [38]
Answer:

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Answer:

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Step-by-step explanation:

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