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ira [324]
2 years ago
14

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However,

records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.(a) What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?Round to 4 decimal.(b) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain gol. On a typical Sunday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager.There is a 10% chance of being at or below a mean oil change time of ? minutes.Round to 1 decimal.
Mathematics
1 answer:
kolezko [41]2 years ago
8 0

Answer:

(a) 0.0128 to 4 decimal places

(b) The 90% confidence interval is 119.1 < μ < 121.0 to 1 decimal places

Step-by-step explanation:

See the attached documents and graphs. Cheers!

Download pdf
<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> pdf </span>
4de97e6d942fe2c9047a396b82fccba0.png
0b940014a3beda8e854506c0084127b3.png
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  • 0.008 °C

Explanation:

<u>1) Write the changes in the temperature of the city over the 4 days in an easy way to read.</u>

<u />

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<u />

<u>2) Write the expression to show the average daily change in temperature.</u>

The average of a set of data is calculated with the expression:

  • Average = (sum of the data) / amount of data

Hence, you need to add the four change of temperature data and divide by 4.

The expression is:

  • Average =  [ 1.34 °C + (- 5 / 7 °C) + ( - 0.75 °C) + 4/9 ° C ] / 4

<u>3) Write the steps to solve the expression:</u>

You can choose between adding  fractions or adding the decimal forms of the numbers.

If you choose adding decimals, keep the complete decimals in your calculator, to avoid the accumulation of errors due to rounding. Round only the final result.

These are the steps.

<u>a. Find the decimal forms of the fractions:</u>

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<u>b. Add the four data:</u>

  • 1.34°C + (- 0.71428 °C) + (-0.75 °C) + 0.44444 °C ≈ 0.32019 °C

<u />

<u>c. Divide the sum by the number of data (4)</u>

  • 0.32019 °C / 4 ≈ 0.080004 °C

<u>4. Round to the nearest hundredth</u>

The place of the hundreth is the second after the decimal point, which is 8 in this case:

  • 0.080004 °C ≈ 0.08 °C

7 0
2 years ago
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