MATH 1530 – Quiz # 7
MATH 1530 – Quiz # 11 (Quizpak 5) Name _____________________________
Assume that the readings on thermometers are normally distributed with a mean of [pic] and a standard deviation of [pic]. One thermometer is randomly selected and tested. In each case, label and shade the graph , then find the probability of getting the stated readings in degrees Celsius. Show the areas to be added or subtracted as read from Table A-2 as well as the solution.
1. Between [pic] and [pic]
[pic] = ___________________________ = ______________
2. Between [pic] and [pic]
[pic] = ___________________________ = ______________
3. Less than [pic]
[pic] = ___________________________ = ______________
4. Greater than [pic]
[pic] = ___________________________ = ______________
MATH 1530 – Quiz # 12 (Quizpak 5) Name _____________________________
Find the missing “z-value” given each of the following probabilities come from a Standard Normal Distribution. In each case, label and shade the graph writing the appropriate probabilities over the shaded region, then state the z-score that provides those probabilities as your solution.
1. If [pic], then [pic]= _____________ .
2. If [pic], then [pic]= _____________ .
3. If [pic], then [pic]= _____________
and [pic] = _____________ .
4. If [pic], then [pic]= _____________ .
MATH 1530 – Quiz # 13 (Quizpak 5) Name _____________________________
Let [pic] be a randomly selected score from a normally distributed population with mean [pic] and standard deviation [pic], then find each of the following probabilities. Label and shade the graphs accordingly. Show the areas to be added or subtracted as read from Table A-2 as well as the solution.
1.
[pic] = [pic] = ___________________ = __________
2.
[pic] = [pic] = ________________________ = ______________
3.
[pic] = [pic] = ________________________ = ______________
4.
[pic] = [pic] = _____________________ = __________
MATH 1530 – Quiz # 14 (Quizpak 5) Name _____________________________
Given a normally distributed population with mean [pic] and standard deviation [pic], find each of the following scores. Label the graphs accordingly. Show formulas and calculations below the graphs.
1. The score that separates the top 40% from the bottom 60%. ______________
2. The score that separates the bottom 10% from the top 90%. ______________
3. The score that separates the top 10% from the bottom 90%. ______________
4. The score that determines the cut-off for the top 25%. ______________
MATH 1530 – Quiz # 15 (Quizpak 5) Name _____________________________
Assume that women’s heights are normally distributed with a mean of [pic] inches and a standard deviation [pic] inches (based on data from the National Health Survey).
1. If 1 woman is selected at random, find the probability that her height is above 63 inches.
P( ) = P( ) = ________________________ = _______________
2. If 100 women are selected at random, find the probability that their mean height is greater than 63 inches.
P( ) = P( ) = ________________________ = _______________
3. Consider the sampling distribution of randomly selecting 100 women at a time and recording the mean heights, then this distribution of sample means has a mean and a standard deviation that are equal to:
(give the numerical values here) [pic] = _______________
[pic] = _______________
MTH 1050 – STATDISK WORKSHEET - CHAPTER 5 Name _______________________
1. a. Use STATDISK to generate 106 values from a normally distributed population with a mean of 98.6 and a standard deviation of 0.62. Use Data/Descriptive Statistics to find the mean of the generated sample.
b. Record the 10 sample means here: (Use decimals = 1 and seed = 1, 2, … , 10)
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
c. After examining those 10 sample means, what do you conclude about the likelihood of getting a sample mean of 98.20? Explain.
_______________________________________________________________________________
_______________________________________________________________________________
d. Given that researchers did obtain a sample of 106 temperatures with a mean of 98.20[pic]F, what does their result suggest about the common belief that the population mean is 98.6[pic]F?
_______________________________________________________________________________
5-2 a. Sample mean: __________ Standard deviation: __________
b. Record the 10 sample means here. (Use decimals = 2 and seed = 1, 2, … , 10)
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
5-3 a. P( ) = _____________________________ = _____________________
b. P( ) = _____________________________ = _____________________
c. P( ) = _____________________________ = _____________________
d. P( ) = _____________________________ = _____________________
e. P( ) = _____________________________ = _____________________
5-5 a. One Die: Mean: __________
(seed = 5) Standard Deviation: __________
Distribution shape: _______________________________
Sketch histogram here.
b. Two Dice: Mean: __________
(seed = 5) Standard Deviation: __________
Distribution shape: _______________________________
Sketch histogram here.
c. 10 Dice: Mean: __________
(seed = 5) Standard Deviation: __________
Distribution shape: _______________________________
Sketch histogram here.
d. 20 Dice: Mean: __________
(seed = 5) Standard Deviation: __________
Distribution shape: _______________________________
Sketch histogram here.
e. General conclusions:
What happens to the mean as the sample size increases from 1to 2 to 10 to 20?
_______________________________________________________________________________
What happens to the standard deviation as the sample size increases?
_______________________________________________________________________________
What happens to the distribution shape as the sample size increases?
_______________________________________________________________________________
How do these results illustrate the central limit theorem?
_______________________________________________________________________________
_______________________________________________________________________________
The following notes will be provided for your reference as the last page of Exam 3:
The Standard Normal Distribution is a normal probability distribution that has a mean of [pic] and a standard deviation of [pic]. (Utilize Table A-2 to find probabilities for given z-scores or to find z-scores for given probabilities.)
Formula for converting x-scores to z-scores:
[pic]
Formula for converting z-scores to x-scores:
[pic]
The Central Limit Thereom:
For large sample sizes (n>30) drawn from ANY distribution (or for smaller sample sizes, if the original distribution is normally distributed), the sampling distribution of the means has the following properties:
1. The distribution of the sample means is approximately Normal.
2. The mean of the sampling distribution is equal to the mean of the population.
[pic]
3. The standard deviation of the sampling distribution is equal to the standard deviation of the population divide by the square root of n.
[pic]
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[pic]
0 z
[pic]
0 z
[pic]
100 x
[pic]
0 z
[pic]
100 x
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
100 x
[pic]
100 x
[pic]
100 x
[pic]
0 z
[pic]
0 z
[pic]
0 z
[pic]
100 x
[pic]
0 z
[pic]
100 x
[pic]
0 z
[pic]
100 x
[pic]
[pic]
[pic]
[pic]
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