Question

1/2.5 points | Previous Answers My Notes You are planning to take to a trip to Montreal, Canada during the month of April and you want to bring clothing that is appropriate for the weather. The daily high temperature X in degrees Celsius in Montreal during April has expected value E(X) - 10.1°C with a standard deviation SD(X) - 4.3°C. You want to convert these Celsius temperatures to F (degrees Fahrenheit). The conversion of X into degrees Fahrenheit Yi Y(9/5)X +32 Question 1. What is E(Y), the expected daily high in Montreal during April in degrees Fahrenheit? Question 2. What is SD(Y), the standard deviation of the daily high temperature in Montreal during April in degrees Fahrenheit? 12.31

Answer 1

Given,

Mean = E(X) = $\mu$ = 10.1

Standard deviation =SD(X) = 4.3

Variance = Var(X) = 4.3^2 = 18.49

The conversion function of X into Y is,

9 Y = -1 + 32

Q1 )

$E(Y) = E\left ( \frac{9}{5}x+32 \right )$

{ since , E(aX + b ) = aE(X) + b }

E(Y)=E(x) +32

E(Y)= x 10.1 + 32

Q2 )

$SD(Y) = \sqrt{Var(Y)}$

Let's find variance first.

$Var(Y) = Var\left ( \frac{9}{5}X+32 \right )$

$Var(Y) = \left ( \frac{9}{5} \right )^2\times Var(X)$ { Since , Var( aX + b ) = a²Var(X) }

$Var(Y) = \frac{81}{25}\times 18.49$

So,

$SD(Y) = \sqrt{Var(Y)}$

$SD(Y) = \sqrt{59.9076 }$