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Session packet
Statistics 226
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Luyun
Stat 226
Anna Peterson
2/7/16
True or false
1) A z-score is a standardized value that tells how many variances the original observation
is off the mean and in which direction.
2) Observations larger than the mean are positive when standardized, and observations
smaller than the mean are negative when standardized.
3) The terms proportion, probability, and area are used interchangeably when working with
the standard normal curve.
4) A z-score is calculated by dividing the difference between the value of an observation
and the mean by the variance.
5) From the formula for a z-score, we can do backward calculations to obtain the value of an
observation.
1. Let Z be a Standard Normal random variable.
Compute
(a) P (Z < 0.97)
(b) P (Z ≤ 0.97)
(c) P (Z > 0.97)
(d) P (|Z| ≤ 0.97)
(e) P (Z < −5.0)
(f) P (Z > −5.0)
2. Let X be a Normal random variable with parameters µ = 8 and σ = 3.5.
Compute
(a) P (X < 0)
(b) P (X > 15)
(c) P (|X| < 2)
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3. TravelByUs is an internet-based travel agency wherein the customers can see videos of
the cities they plan to visit. The number of daily hits at its website is Normally distributed
with
µ = 1, 000 and σ = 240.
(a) What is the probability of getting fewer than 900 hits?
(b) The website of this company has a limited bandwidth, which is measured in terms of
the number of hits the site can handle. How large a bandwidth should TravelByUs
have in order to handle 99% of the daily traffic?
4. The scoring of modern IQ tests is such that Intelligence Quotients (IQs) have Normal
distribution with µ = 100 and σ = 15.
(a) What percent of people have IQ less than 80?
(b) What percent of people have IQ greater than 120?
(c) Mensa International is a non-profit organization that accepts only people with IQ
within the top 2%. What level of IQ qualifies one to be a member of Mensa?
5.
Among all the computer chips produced by a certain factory, it follows a normal
distribution. The mean defective chip is 24 and the standard deviation of the defective
chips is 2.
(a) What is the probability that this sample contains between 20 and 25 defective chips
(including 20 and 25)?
(b) How many defective chips is included into 0.67 percentile of all the chips?
6. The BMI for males age 20 to 74 is follows approximately a normal distribution with
mean μ = 27.9 and standard deviation σ = 7.8. Use the 68-95-99.7 rule to find
1) The percentage of males with BMI less than 20.1.
2) The percentage of males with BMI greater than 12.3.
3) The BMI values that correspond to the middle 99.7% of the distribution.
4) The value such that 0.15% of males have BMI’s greater than the value.
7. The annual salaries of employees in a large company are approximately normally
distributed with a mean of $50,000 and a standard deviation of $20,000.
a) What percent of people earn less than $40,000?
b) What percent of people earn between $45,000 and $65,000?
c) What percent of people earn more than $70,000?