Introduction to Normal Distribution

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Show your work for each problem.

1.
What shape does the normal distribution have?
1. a)J-shaped (skewed right)
2. b)U-shaped
3. c)Bell-shaped (symmetric)
4. d)Uniform (flat)
2.
In a normal distribution, which percentage of data falls within 1 standard deviation of the mean?
1. a)68%
2. b)95%
3. c)99.7%
4. d)50%
3.
In a normal distribution, what percentage of data falls within 2 standard deviations of the mean?
4.
In a standard normal distribution, what are the values of the mean () and standard deviation ()?
1. a),
2. b),
3. c),
4. d),
5.
A student scores 75 on a test with mean and standard deviation . What is the z-score?
6.
A data point has value in a distribution with and . What is the z-score?
7.
Heights are normally distributed with cm and cm. What percentage of people are between 158 cm and 182 cm?
1. a)68%
2. b)95%
3. c)50%
4. d)99.7%
8.
Test scores are normally distributed with and . Find the z-score for a student who scored 680.
9.
Weights of packages are normally distributed with kg and kg. If a package has a z-score of , what is its weight?
10.
A z-score of means the value is:
1. a)1.5 standard deviations below the mean
2. b)1.5 times the mean
3. c)1.5 standard deviations above the mean
4. d)At the 1.5th percentile
11.
Battery life is normally distributed with hours and hours. What battery life corresponds to the 84th percentile (z-score )?
12.
In a normal distribution with and , what value has a z-score of ?
13.
IQ scores are normally distributed with and . What range of IQ scores contains the middle 68% of the population?
14.
In a normal distribution, what percentage of data is MORE than 2 standard deviations above the mean?
1. a)2.5%
2. b)2.15%
3. c)5%
4. d)16%
15.
Exam scores are normally distributed with and . Student A scores 88 and Student B scores 64. Who performed better relative to the class, and by how much?