In: Statistics and Probability
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.7 ppm and standard deviation 1.6 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
a) X ~ N(9.7, 1.6)
b) = 9.7
= 1.6/ = 0.2596
~ N(
c) P(X < 10.4)
= P((X - )/ < (10.4 - )/)
= P(Z < (10.4 - 9.7)/1.6)
= P(Z < 0.44)
= 0.6700
d) P( < 10.4)
= P(( - )/() < (10.4 - )/())
= P(Z < (10.4 - 9.7)/(1.6/))
= P(Z < 2.70)
= 0.9965
e) No, since the sample size is greater than 30, so it is not necessary to assume that the distribution is normak.
f) P( < x) = 0.25
or, P(( - )/() < (x - )/()) = 0.25
or, P(Z < (x - 9.7)/(1.6/)) = 0.25
or, (x - 9.7)/(1.6/) = -0.67
or, x = -0.67 * (1.6/) + 9.7
or, x = 9.526
Q1 = 9.526
P( < x) = 0.75
or, P(( - )/() < (x - )/()) = 0.75
or, P(Z < (x - 9.7)/(1.6/)) = 0.75
or, (x - 9.7)/(1.6/) = 0.67
or, x = 0.67 * (1.6/) + 9.7
or, x = 9.874
Q3 = 9.874
IQR = Q3 - Q1 = 9.874 - 9.526 = 0.348