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Cool pool? Coach Ferguson uses a thermometer to measure the temperature (in degrees Celsius) at 20different locations in the school swimming pool.

An analysis of the data yields a mean of25Cand a standard deviation of 2C. Find the mean and standard deviation of the temperature readings in degrees Fahrenheit (recall that F=(9/5)C+32)

Short Answer

Expert verified

The mean temperature is u=77Fand the standard deviation is=3.6F

Step by step solution

01

Step 1. Given

Mean =25C

Standard deviation =2C

02

Step 2. Concept

The sample standard deviation is measured in the same units as the original data.

03

Step 3. Calculation

We have 渭 = 25Cand =2C

Also we know that F=(95)C+32......(1)

Temperature conversion from Celsius to Fahrenheit

The following formula is used to compute the pool's average temperature in Fahrenheit:=25C=(95)25+32(usingequation(1))=77F

We just multiply the standard deviation in degrees Celsius by 95 to get the standard deviation. Because the addition of32 only changes the distribution and has no effect on the spread, we get:=2C=952=3.6F

As a result, the swimming pool's mean temperature is u=77F, and the standard deviation is =3.6F

Therefore, the mean temperature is u=77F and the standard deviation is =3.6F

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