Question

Find the minimum sample size n needed to estimate μ for the given values of c,σ, and E. c=0.98,σ=5.1, and E=1 Assume that a preliminary sample has at least 30 members. n= (Round up to the nearest whole number.)

Answer 1

Answer: about 141

Explanation:

To find the minimum sample size (n) needed to estimate μ, we can use the formula:

n = (Z * σ / E)^2

Where:

n is the sample size

Z is the Z-score corresponding to the desired confidence level (c)

σ is the population standard deviation

E is the desired margin of error

In this case, we have the following values:

c = 0.98 (confidence level)

σ = 5.1 (population standard deviation)

E = 1 (margin of error)

Now, let's calculate the minimum sample size (n) using the formula mentioned above.

First, we need to find the Z-score corresponding to a confidence level of 0.98. Since the confidence level is 0.98, the area under the normal distribution curve outside the interval is (1 - c) / 2 = 0.01. Looking up this value in the Z-table, we find that the Z-score is approximately 2.33.

Now, we can substitute the values into the formula:

n = (2.33 * 5.1 / 1)^2

Simplifying the expression:

n = (11.883 / 1)^2

n = 11.883^2

n ≈ 141

Therefore, the minimum sample size needed to estimate μ, given the values of c = 0.98, σ = 5.1, and E = 1, is approximately 141.