a research scholar wants to know how many times per hour a certain strand of virus reproduces. he wants to construct the 95% confidence interval with a maximum error of 0.22 reproductions per hour. assuming that the mean is 9.7 reproductions and the standard deviation is known to be 2.4, what is the minimum sample size required for the estimate? round your answer up to the next integer.

A researcher is interested in learning how frequently a specific virus strand reproduces each hour. With a maximum inaccuracy of 0.22 reproductions per hour, he seeks to create the 95% confidence interval.

We have to find what minimum sample size is needed for the estimate if the mean is 9.7 reproductions and the standard deviation is known to be 2.4.

The mean of the sample ∑x = 9.7

The standard deviation of population σ = 2.4

Sample size n =0.22

The 95% of confidence intervals,

(∑x - Zₐ (S.D/√n),∑x + Zₐ (S.D/√n))

(9.7-1.28(2.4/√0.22),9.7+1.28(2.4/√0.22))

(3.15,16.24)

Therefore, The minimum sample size is needed for the estimate if the mean is 9.7 reproductions and the standard deviation is known to be 2.4 is 3.15.

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