Step by step solution to "question 2"

Braydon Bowie

Answered question

2022-03-24

question 2

Answer & Explanation

Ian Adams

Skilled2022-04-21Added 163 answers

Step 1
Given:
$[μ_{y} = 16.6 + 1.02 x r i > h]$ (Equation population regression line)
$[σ = 6.64]$
The average high temperature on days where the low temperature is $40^{\circ}$ F according to the population regression line can be found by replacing 2 in the regression line equation by 40 and evaluating.
$[μ_{y} = 16.6 + 1.02 (40) = 16.6 + 40.8 = 57.4]$
Thus the mean is 57.4 and the standard deviation is 6.64.
Since the conditions are met, the response y varies according to a Normal distribution.
The z-score is the value decreased by the mean, divided by the standard deviation.
$[z = \frac{x - μ}{σ} = \frac{70 - 57.4}{6.64} \approx 1.90]$
Determine the corresponding probability using the normal probability table in the appendix. $[P (Z < 1.90)]$ is given in the row starting with 1.9 and in the column starting with .00 of the standard normal probability table in the appendix.
$P (X > 70) = P (Z > 1.90)$
$= 1 - P (Z < 1.90)$
$= 1 - 0.9713$
$= 0.0287$
$= 2.87 %$
Thus about 2.87% of the days with a low temperature of $40^{\circ}$ F are expected to have a high temperature that is greater than $70^{\circ}$ F.
Result: 2.87%

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