please answer the question with a detaild answer thanks The

please answer the question with a detaild answer thanks

The noon-time temperature of seven randomly selected days of August in a coastal site of Spain gives x = 31 C degree and S = 1.5C degree. The formula for converting a measurement in the Celsius scale to the Fahrenheit scale is F degree = 1.8C degree + 32. Find the sample mean and variance of the seven temperature measurements when expressed in the Fahrenheit scale.

Solution

Given that mean = 31 degree Celcius

Let C be the temperature in centigrade

E(C) = 31 and Var(C) =1.5²

We have to find E(F) and Var(F)

E(F) = E(1.8C+32)

= 1.8E(C)+32

=55.8+32

= 87.8 degree F

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Var(F) = Var(1.8C+32)

= 1.8²Var(C)

= 3.24(1.5)

=4.86

Hence std dev (F) = 2.205 degree F