Question

Suppose that the average bill for the drive through of 24 customers at Burger Palace is $14.30. It is known that the population standard deviation is σ=2.30. Estimate the true mean bill for a customer at Burger Palace with 95% confidence.

Answer 1

The standard deviation is a measure of a collection of values' variance or dispersion. The true mean bill for a customer at Burger Palace with 95% confidence is $13.38.

What is a standard deviation?

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Given that the Sample mean ($\overline x$) is $14.30, the Sample size(n) is 24 customers, the Standard deviation(σ) is 2.30, while for a 95% confidence interval the Z-score is 1.960. Therefore, the true mean can be written as,

$Z = \dfrac{\overline x- \mu}{\frac{\sigma}{\sqrt n}}\\\\\\1.960 = \dfrac{14.30-\mu}{\frac{2.30}{\sqrt{24}}}\\\\\\1.960 = \dfrac{14.3-\mu}{0.47}$

μ = 13.3788 ≈ 13.38

Hence,  the true mean bill for a customer at Burger Palace with 95% confidence is $13.38.

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