Question

Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 5% at the 95% confidence level, how many randomly selected teenagers must we survey?

If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)

Answer 1

Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 5% at the 95% confidence level, how many randomly selected teenagers must we survey?

If we have not given a prior estimate we take p = 0.5 for unbiasedness.

Margin of error = E = 0.05

Confidence level = C = 0.95

Zc = 1.96 ( Using z table)

p = 0.50

We have to find sample size (n)

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If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)

Probability = p = 0.15

Sample size = 350

We have to find the probability that fewer than 42 adults will work from home.

That is we have to find P(X < 42)

P(X < 42) = 1 - P(X 41) = 1 - 0.0464 = 0.954

( Using excel =BINOMDIST(41,350,0.15,1))