How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has length less than 0.1, 0.05, and 0 .01, respectively

(1) 97

(2) 385

(3) 9604

Step-by-step explanation:

The (1 - α) % confidence interval for population proportion is:

The margin of error in this interval is:

The formula to compute the sample size is:

(1)

Given:

*Use the z-table for the critical value.

Compute the value of n as follows:

Thus, the minimum sample size required is 97.

(2)

Given:

*Use the z-table for the critical value.

Compute the value of n as follows:

Thus, the minimum sample size required is 385.

(3)

Given:

*Use the z-table for the critical value.

Compute the value of n as follows:

Thus, the minimum sample size required is 9604.

x/3-10=8

x/3=18

x=48