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Let Z be the reading on thermometer. Z follows Standard Normal distribution with mean μ =0 and standard deviation σ=1
The probability that randomly selected thermometer reads greater than 2.07 is
P(z > 2.07) = 1 -P(z < 2.07)
Using z score table to find probability below z=2.07
P(Z < 2.07) = 0.9808
P(z > 2.07) = 1- 0.9808
P(z > 2.07) = 0.0192
The probability that a randomly selected thermometer reads greater than 2.07 is 0.0192
The formula for depreciation is:
Where x = Initial value,
y= Amount after depreciation.
r= Rate of depreciation,
t = time (in years)
According to given problem,
x = 1040, y= 944 and t = 12 months =1 year.
So, first step is to plug in these values in the above formula, So,
944 = 1040 (1 -r)
Divide each sides by 1040.
0.907692308 =1 - r
0.907692308 - 1 = -r Subtract 1 from each sides.
-0.092307692 = -r
So, r = 0.09 or 9%.
Now plug in 0.09 in the above equation to get the depreciation equation. So,
So,
b) To find the value of the bike after 5 months,
plug in t = 5 months= 5/12 = 0.41667 years in the above equation of depreciation.
So,
y = 1040 * 0.961465659
y = 999.9242852
y = 1000 (Rounded to nearest integer).
Hence, the value of the bike after 5 months is $1000.