Question

fast-food bills for drive-thru customers a random sample of 41 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $17.15 per car. the population standard deviation is $4.94. estimate the mean bill for all cars from the drive-thru with 91% confidence. round intermediate and final answers to two decimal places.
$□ < μ < $□

Explanation:

Step1: Identify given values

Sample size $n=41$, sample mean $\bar{x}=17.15$, population standard deviation $\sigma=4.94$, confidence level 91%.

Step2: Find z-score for 91% confidence

Significance level $\alpha=1-0.91=0.09$, so $\alpha/2=0.045$. The z-score for $1-0.045=0.955$ cumulative probability is ~1.695.

Step3: Calculate standard error

Standard error $SE=\frac{\sigma}{\sqrt{n}}=\frac{4.94}{\sqrt{41}}\approx\frac{4.94}{6.403}\approx0.7715$.

Step4: Compute margin of error

Margin of error $E=z\times SE\approx1.695\times0.7715\approx1.308$.

Step5: Find confidence interval

Lower bound: $\bar{x}-E\approx17.15-1.308\approx15.84$; Upper bound: $\bar{x}+E\approx17.15+1.308\approx18.46$.

Answer:

15.84 < μ < 18.46