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)

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b.

a.

c.

0.4772

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