Assume that daily high temperatures in Fort Collins in July follow a normal dist
ID: 3229420 • Letter: A
Question
Assume that daily high temperatures in Fort Collins in July follow a normal distribution with a mean of 87 degrees Farenheit and a standard deviation of 3 degrees.
a) What daily high July temperature is two-thirds standard deviations below the mean?
b) What is the probability that the hight temperature on one randomly selected July day is higher than 90 degrees?
c) Find two temperatures such that 95% of July days will have a high temperature between these two values.
d) Calculate the IQR of this distribution.
Explanation / Answer
a) for 2/3 std deviation below mean has zscore =-2/3
hence corresponding temerature =mean +z*std deviation= 87-(2/3)*3=85 degree
b)P(X>90) =1-P(X<90|)=1-P(Z<(90-87)/3)=1-P(Z<1)=1-0.8413=0.1587
c)for 95% CI, z=1.96
hence LCL, UCL =(mean -/+z*std deviation)=81.12 ; 92.88
d)IQR lies b/w 25 and 75 percentile for which z score =0.6745
hence LCL, UCL =(mean -/+z*std deviation)=84.98 ; 89.02