Download Chapter 6 Graded HW Assignment Name: Directions: For each

Chapter 6 Graded HW Assignment
Name:_______________________________
Directions: For each problem, draw a diagram and/or write down calculator inputs. Round answers
as indicated.
1.
The Precision Scientific Instrument company manufactures thermometers that are supposed to
give readings of 0°C at the freezing point of water. Tests on a large sample of these
thermometers reveal that at the freezing point, some give readings below 0°C and some give
readings above 0°C. Assume that the mean reading is 0°C and the standard deviation of the the
readings is 1.0°C. The frequency distribution of errors closely resembles the normal distribution.
(a) A quality control analyst wants to examine thermometers that give readings in the bottom
4%. Find the reading that separates the bottom 4% from the others. (Round to the nearest
hundredth)
(b) What is the probability that if a thermometer is randomly selected, that it gives a reading
between -1.5°C and 2.25°C ? (round to the nearest hundredth)
(c) What is the probability that a thermometer records above 2°C ? (round to the nearest
hundredth)
2.
If the mean of a normal distribution is 60 and the standard deviation is 4, what is the probability
that a score will be less than 53? (round to the nearest hundredth)
3.
The monthly incomes of trainees at a local warehouse are normally distributed with a mean of
$1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a
month? (round to the nearest tenth)
4.
Scores on a test are normally distributed with a mean of 63.9 and a standard deviation of 10.9.
Find the value of the 80th percentile. (round to the nearest tenth)
5.
What is the probability that a z-score is less than 1.28?(round to the nearest hundredth)
6.
A final exam in Math has a mean of 73 with a standard deviation of 7.8. What is the
probability that a randomly selected student has a grade that is at least an 80? (round to the
nearest hundredth)
7.
Assume that women’s heights are normally distributed with a mean of 63.6 inches and a
standard deviation of 2.5 inches. What are the women’s heights at the bottom 10% and at the
top 10%? (round to the nearest tenth)
8.
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. In a
random sample of 9000, approximately how many people will have IQs between 85 and 120?
(Hint: calculate the percent first)
9. (a) In one region, the September energy consumption levels for single-family homes are found
to be normally distributed with a mean of 1050 KWh and a standard deviation of 218 kWh. Find
the probability that a randomly selected home would have an energy consumption level less
than 1075 kWh. (round to the nearest hundredth)
(b) If 25 homes were selected, what is the probability that the consumption was more than
1100?
10. The adult population has a mean IQ of 100 and a standard deviation of 15 points.
(a) What is the probability of a person having an IQ between 90 and 110?
(b) What is the probability that a group of 30 adults have a mean IQ greater than 115?
(c) In general, what IQ represents the 90th percentile?