If I were studying for a test
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Calculator For Chapter 7
2nd DISTR
To find a probaility of a normal distribution:
2: normalcdf (lower, upper, mean, standard error)
Standard Error = σ/[pic]
To input “infinity” use E99 (2nd with comma key to access E)
To input “negative infinity” use – E99 (2nd with comma key to access E)
Three probability forms:
[pic] use 2: normalcdf (a, b, mean, standard error)
[pic] use 2: normalcdf (a, E99, mean, standard error)
[pic] use 2: normalcdf (– E99, b, mean, standard error)
To find a position, given a percentile:
3: invnorm(area, mean, standard deviation)
area = percentile (% to the left or below this position)
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a. 2:normalcdf ( 0, 1, 0, 1) b. 2:normalcdf (0, 1.58, 0, 1)
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c. 2:normalcdf (1.20, 2.30, 0, 1)
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2:normalcdf( 1.27, E99, 0, 1)
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2:normalcdf (– E99, – 1.27, 0, 1)
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2:normalcdf (0, 1.58, 0, 1)
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2:normalcdf (– 2.43, 0, 0, 1)
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2:normalcdf (143, 201, 143, 29)
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2:normalcdf (150, E99, 143, 29 )
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2:normalcdf (150, E99, 143, 29/[pic] )
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2:normalcdf (150, E99, 143, 29/[pic] )
Quick Quiz 6
1. Use the probability distribution below to answer the following:
x 0 1 2 3 4
P(x) 0.05 0.25 0.45 0.15 0.10
P( x = 2)
P(x < 2)
Probability x is at least 2
2. The probability of guessing right on a 5-option multiple choice item is 1/5 or 0.2.
If a quiz contains 5 questions:
What is the probability of getting none right?
What is the probability of passing (getting 3, 4, or 5 right)?
3. The contents of cereal boxes are normally distributed, with a mean of 20 oz and a
standard deviation of 0.07 oz.
What is the probability of getting a value between 19.86 and 20.14 oz?
What is the probability of getting a value less than 20.1 oz?
4. The mean height for men is 69.2 inches, with a standard deviation of 2.9 inches. If a
random sample of 60 men is selected, what is the probability that their mean height is greater than 70 inches?
Answers:
1. P (x = 2) = 0.45, P (x < 2) = 0.3, P(x ≥ 2) = 0.7
2. P (x = 0) = 0.328, P (x ≥ 3) = 0.058
3. P (19.86 ≤ x ≤ 20.14) = 0.95, P (x < 20.1) = 0.923
4. P (x ≥ 70) = 0.0163
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3:invnorm (.95, 0, 1)
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3:invnorm (.10, 0, 1)
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3:invnorm (.10, 143, 29)
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3:invnorm (.99, 143, 29)
Quick Quiz 7
WARNING: answers may not match the choices exactly depending on the method used for solving! Select the closest answer.
Assume that the freezing point for water is normally distributed and has a mean of 0◦ Celsius and a standard deviation of 1.
1. What temperature reading separates the bottom 7% from the others?
a. -1.89 b. 1.48 c. 1.89 d. -1.48
2. Find the probability of getting a reading between 0.7 and 1.98
a. -0.2181 b. 0.2175 c. 0.2181 d. 1.7341
3. Find the probability of getting a reading greater than -1.82
a. 0.4656 b. 0.0344 c. 0.9656 d. -0.0344
4. Assume x has a normal distribution with a mean of 40 and standard deviation of 12.
What is the probability that x is less than 46.
a. 0.3830 b. 0.6170 c. 0.3085 d. 0.6915
5. 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 81st percentile.
a. 67.1 b. 0.291 c. 73.5 d. 0.88
6. Incomes for workers are normally distributed with a mean of $1100 and a standard
deviation of $150. What percentage of workers earns less than $900 a month?
a. 40.82% b. 9.12% c. 35.31% d. 90.82%
Answers:
1. d 2. c 3. c 4. d 5. c 6. b
If I were studying for a test
on Chapter 7, these are the things
I would be sure to know
Assume that a distribution has a mean of 0 and a standard deviation of 1.
1. What is the probability that z is:
a. Between 0 and -2.33 (.4901)
b. Greater than 2.05 (.0202)
c. Between 0.27 and 2.27 (.3820)
d. Between -2.73 and 2.51 (.9908)
2. 95% of the scores fall below what value? (1.64)
3. What value separates the top 40%? (0.25)
Assume that IQ's have a mean of 100 and a standard deviation of 15.
5. What is the probability that x is:
a. Between 88 and 112 (.5763)
b. Between 120 and 130 (.0685)
c. Greater than 140 (.0038)
6. What IQ separates the top 1% from the other scores? (135)
7. If 36 people are selected, find the probability that
their mean will be between 100 and 105. (.4772)
8. In a normal distribution the mean is 500 with a standard deviation of 100. What is the standard
error for a group of size 25? (20)
9. A study of DVD owners found that their annual household incomes are normally distributed
with a mean $41,182 and standard deviation of $19,990.
a. What is the probability a random household has an income between
$30,000 and $50,000? (.3825)
b. If an advertising campaign is to be targeted at those DVD owners
whose incomes are in the top 90%, find the minimum income level for
this target group. ($15,564)
10. College freshmen study an average of 7.06 hours per week with a standard deviation of 5.32
hours. If 55 freshman are randomly selected, find the probability that their mean weekly
study time will exceed 7 hours. (.5333)
11. The heights of men have a mean of 69.0 inches and a standard deviation of 2.8 inches. If 95% of males meet the minimum height requirement for police officers, what is that
minimum height requirement? (64.4)
12. A population has a mean of 4.50 and a standard deviation of 1.05
a. Find the probability that 1 person's score is less than 5.00. (.6830)
b. Find the probability that the mean of 40 people's scores is less than 5.00. (.9987)
-----------------------
b.
a.
c.
0.4772
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