Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name and your lab time. Show all work and round answers to at least 3 decimal places.
1. The wingspans of adult seaside sparrows (Ammodramus maritimus) follow a normal distribution with a mean of 6.5 inches and a standard deviation of 0.3 inches.
a. Sketch the distribution of seaside sparrow wingspans. Be sure to include labels and an accurate scale. (2pt)
b. Between which two wingspan measurements are the middle two quartiles of the distribution? (3pt)
c. Suppose you randomly select 5 seaside sparrows. What is the probability that none of them have a wingspan of over 6.75 inches? (3pt)
2. Suppose a farmer has many strawberry plants of two different varieties: 40% are variety A and 60% are variety B. The yield for variety A plants is approximately normally distributed, with a mean of 28 oz and a standard deviation of 4 oz. The yield for variety B plants is also approximately normal, with a mean of 35 oz and a standard deviation of 7 oz.
a. Overall, what proportion of her plants yield more than 30 oz? (5pt)
b. If you randomly select a plant that yielded less than 30 oz, what is the probability that it was variety A? (4pts)
3. Researchers have discovered a new genetic marker for a form of cancer. Twelve percent of the overall population carry this marker, and of all the people who develop this cancer, 38% carry the marker. Suppose that the total frequency of cancer incidents in the population is 2.2%. What is the probability that a person with the marker develops cancer? (3pt)