Question

Suppose that a customer service center claims that the telephone calls it receives last 114 seconds on average, with a standard deviation of 9 second. If you took a sample of 324 telephone calls, which of the following mean times would be within the 95% confidence interval

Answer 1

The answer would be 114.5 seconds

-- i got it right in the quiz, good luck (:

Answer 2

Using Normal distribution, mean times would be within 95% confidence intervals is 114.5.

What is Normal distribution?

Normal distribution is "a continuous probability distribution that its symmetrical about its mean with most values near its central peak".

According to the question,

On average, calls received last 114 seconds with standard deviation of 9 seconds and sample have 324 telephone calls.

From given data, Average (μ) = 114 seconds

standard deviation (σ) = 9 seconds

Formula for 95% confidence interval in normal distribution is 1.96.

(x⁻  - z * σ/√n, x⁻ - z* σ/√n)

(114 - 1.96* (9/$\sqrt{324}$), 114 - 1.96* 9/$\sqrt{324}$ )

(114 - 1.96*(9/18), 114 - 1.96*(9/18) )

(114 - 1.96*(1/2), 114 - 1.96*(1/2))

(114 - 0.98, 114 + 0.98)

(113.02,114.98)

Hence, mean times would be within 95% confidence intervals in normal distribution is 114.5. The value 114.5 lies between interval (113.02,114.98).

Learn more about Normal distribution here

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