Question

1) A sample of 49 units drawn from a normally distributed population results in a sample mean of 18 and sample variance of 4. Use the t-distribution to find the 90% confidence interval for the mean. What is the upper limit?

2) A casino has a biased coin that lands on heads 60% of the time. It pays out $10 every time the coin lands on tails and nothing if it lands on heads. What is the expected payout for the coin?

Answer 1

#1.
sample mean, xbar = 18
sample standard deviation, s = 2
sample size, n = 49
degrees of freedom, df = n - 1 = 48

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.677

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (18 - 1.677 * 2/sqrt(49) , 18 + 1.677 * 2/sqrt(49))
CI = (17.52 , 18.48)

Upper limit = 18.48

#2.
Expected payout = (1-0.6)*10 = $4