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A chemist measures the temperature of a solution in °C. The measurement is denoted C, and is normally distributed with mean 40°C and standard deviation 1°C. The measurement is 1.8C32. What is the distribution of F? a) F N(104,3.24) b) F N(104,1.80) c) F N(40,3.24) d) F N(40,1.80)

Sagot :

SakshiRa

Measurement of temperature by Chemist involving Mean and SD:

The distribution of F is (a) F = N(104, 3.24).

What is Mean and Standard deviation?

A  mean is calculated by dividing the total number of values by the sum of all the values. The term "average" is frequently used to describe this measure of central tendency.

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilized. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

Calculation:

As,E[ax+b]=aE(x)+b

Var(ax+b)=a∧2(Var(x))

Now, F=1.8C+32

E(F)=1.8×E(C)+32=1.8×40+32

E(F)=104

Var(F)=1.82×1=3.24

std_dev(F)=√(3.24)=1.8

So, F ≈ N(104,3.24).

Measurement of temperature by Chemist involving Mean and SD:

The distribution of F is (a) F = N(104, 3.24).

To refer more about Standard deviation visit:

https://brainly.com/question/475676

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