1. Let X1,..., Xn  be a random sample from an exponential distribution with parameter θ. A sample of 350 observations from this population has a mean equal to 3.75. Construct a 90% con?dence interval for θ.

2. Suppose the population is women at least 35 years of age who are pregnant with a fetus affected by Down syndrome. We are interested in testing positive on a noninvasive screening test for fetuses affected by Down syndrome in women at least 35 years of age. In an experiment, suppose 52 of 60 women tested positive. Obtain a 95% con?dence interval for the true proportion of women at least 35 years of age who are pregnant with a fetus affected by Down syndrome who will receive positive test results from this procedure.