Download Review Problems 6.1 6.2

PSU Stat 243; Review of sections 6.1 and 6.2
Due at the end of your class period on Thursday Dec 4, 2014
Record a full solution, as outlined in class, to each on separate paper and turn in as
assignment “REVIEW 6.1-6.2”. Save this worksheet for when you study for the test.
1. GPAs of SUNY Oswego freshman biology majors have approximately
the normal distribution with mean 2.87 and standard deviation .34.
a. In what range do the middle 90% of all freshman biology majors’
GPAs lie?
b. Students are required to attend tutorial sessions if their GPA falls
below 2.00. What proportion of all freshman biology majors are
required to attend tutorial sessions?
c. What proportion of freshman biology majors have GPA above
3.50?
2. The length of elephant pregnancies from conception to birth varies
according to a distribution that is approximately normal with mean 525
days and standard deviation 32 days.
a. What percent of pregnancies last more than 20 months?
b. What percent of pregnancies last between 510 and 540 days?
c. How short do the shortest 10% of all pregnancies last?
3. Wingspans of adult herons have approximate normal distribution with
mean 125 cm and standard deviation 12 cm.
a. What proportion of herons have wingspan more than 140 cm?
b. What is the median wingspan?
c. What are the first and third quartiles of the wingspans? Hint: think
of the relationship between quartiles and percent of data.
4. When robins’ eggs are weighed, it turns out that they vary according to
approximately the normal distribution with mean 17.5 mg and standard
deviation 3.5 mg.
a. What proportion of robins’ eggs weigh between 10 mg and 25
mg?
b. How large are the largest 2% of all robins’ eggs?
Exercises
1. A forest products company claims that the amount of usable lumber in
its harvested trees averages 172 cubic feet and has a standard
deviation of 12.4 cubic feet. Assume that these amounts have
approximately a normal distribution.
a. What proportion of trees contain more than 150 cubic feet?
b. What proportion of trees contain between 175 and 190 cubic feet?
2. At two years of age, sardines inhabiting Japanese waters have a length
distribution that is approximately normal with mean 20.20 cm and
standard deviation 0.65 cm.
a. What proportion of these sardines are between 19.0 and 21.0 cm
long?
b. How long are the longest 15% of all these sardines?
c. How short are the shortest 15% of all these sardines?
d. In what range do the middle 70% of all sardines fall?
3. The mean cholesterol level in children is 175 mg/dL with standard
deviation 35 mg/dL. Assume this level varies from child to child
according to an approximate normal distribution.
a. What percentage of children have a cholesterol level above 200
mg/dL?
b. How high are the levels for the highest 2% of all children?
4. Porphyrin is a pigment in blood protoplasm and other body fluids that is
significant in body energy and storage. In healthy Alaskan brown bears,
the amount of porphyrin in the bloodstream (in mg/dL) has approximate
normal distribution with mean 47.5 and standard deviation 12.2.
a. What proportion of these bears have between 27.5 and 67.5
mg/dL porphyrin in their bloodstream? (That’s within 20 of the
mean amount of 47.5.)
b. How low are the porphyrin levels for the lowest 3% of all the
bears?
5. Healthy 10-week-old domesticated kittens have average weight 24.5 oz.
with a standard deviation of 5.25 oz. The distribution is approximately
normal.
a. A kitten is designated as dangerously underweight when, at 10
weeks, it weighs less than 10.0 oz. What proportion of healthy
kittens will designated as dangerously underweight?
b. What is the median weight of the kittens?
c. What are the first and third quartiles of the kitten weights?