Find the minimum sample size $n$ needed to estimate $μ$ for the given values of $c, σ$ , and $E$ .
$c = 0.90, σ = 8.7, and E = 2$
Assume that a preliminary sample has at least 30 members.
$n =$
(Round up to the nearest whole number.)

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Answer

So, the minimum sample size n needed to estimate μ for the given values of c, σ, and E is $52$ .

Steps

Step 1 ：Given values are: confidence level c = 0.90, standard deviation σ = 8.7, and margin of error E = 2.

Step 2 ：The z-score Zc corresponding to the confidence level c = 0.90 is 1.645 (for a two-tailed test).

Step 3 ：The formula to calculate the sample size n is given by: $n = {(\frac{Z_{c} * σ}{E})}^{2}$

Step 4 ：Substitute the given values into the formula: $n = {(\frac{1.645 * 8.7}{2})}^{2}$

Step 5 ：Calculate the sample size n to get n = 52.

Step 6 ：So, the minimum sample size n needed to estimate μ for the given values of c, σ, and E is $52$ .