Answer:
[tex]40.97<\mu<43.03[/tex]
Step-by-step explanation:
Th formula for calculating the confidence interval of a population is expressed as shown;
CI = xbar ± Z*S/√n where;
xbar is the mean or average sample
Z is the z-score at 90% confidence
S is the standard deviation
n is the sample size
Given parameters
xbar = 42
Z at 90% CI = 1.645
S = 5
n = 64
Substituting the values into the formula will give;
CI = 42±(1.645*5/√64)
CI = 42±(1.645*5/8)
CI = 42±(1.645*0.625)
CI = 42±1.028125
CI = (42-1.028125, 42+1.028125)
CI = (40.971875, 43.028125)
Hence the 90% confidence interval for the population is approximately (40.97, 43.03) i.e [tex]40.97<\mu<43.03[/tex]
