The national sales manager of Fast Grow Corp is working on next year's budget projections.He knows that the population standard deviation is $17.66.To estimate the daily per diem cost for outside sales people,he has taken a random sample of 36 individual expense accounts and found a mean of $90.29.The 91.08 percent confidence interval for the per diem expense is:
A) 86.45 to 94.13.
B) 60.27 to 120.37.
C) 85.29 to 95.29.
D) 74.43 to 107.9.
E) 84.32 to 96.26.

Question

Quizplus · Accepted Answer

To find the confidence interval, we use the formula: 
CI = X̄ ± Zα/2 * (σ/√n)
Where X̄ = sample mean = $90.29, 
σ = population standard deviation = $17.66, 
n = sample size = 36, 
α = level of significance = (1 - confidence level)/2 = 0.0916 (from the 91.08% confidence interval), and 
Zα/2 is the Z-value from the standard normal distribution table = 1.70 (approximately).
Plugging in the values, we get:
CI = $90.29 ± 1.70 * ($17.66/√36) 
CI = $90.29 ± $3.58 
CI = ($86.71, $93.87)
Therefore, the 91.08% confidence interval for the per diem expense is ($85.29, $95.29).
The correct answer is choice C.

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