7-3- The Normal Distribution

Fill in the Blanks

What is the main objective mentioned in the slide?

Multiple Choice

What is a normal distribution?

• A distribution with a single peak

• A symmetric, bell-shaped curve

• A distribution with two peaks

• A skewed distribution

Multiple Choice

What is the difference between a skewed left and a skewed right distribution?

• Skewed left has a tail on the left; skewed right has a tail on the right

• Skewed left has a tail on the right; skewed right has a tail on the left

• Both have tails on the left

• Both have tails on the right

Open Ended

Explain how to calculate the values defined by the standard deviation in a normal distribution.

Fill in the Blanks

The weight of a box of cereal averages

grams with a standard deviation of 5 grams.

Multiple Choice

According to the Empirical Rule, what percentage of data falls within 2 standard deviations from the mean?

• 68.3%

• 95.5%

• 99.7%

• 50%

Open Ended

Estimate how many patients healed in the interval 200-280 hours if a hospital treated 2000 patients.

Multiple Choice

How many boxes fall within each of the following intervals?

• 560-570 grams

• 555-575 grams

• 550-580 grams

Open Ended

Explain how a change in the standard deviation affects the shape of the normal distribution curve.

Fill in the Blanks

The normal distribution has two parameters: the mean (µ) and the

(σ).

Multiple Choice

What is the significance of the bell-shaped curve in a normal distribution?

• It represents the mean value.

• It shows the distribution of data around the mean.

• It indicates the maximum value.

• It highlights the minimum value.

Multiple Choice

What does a z-score tell you about a data point in a normal distribution?

• Its absolute value.

• Its position relative to the mean.

• Its frequency in the dataset.

• Its maximum possible value.

Multiple Choice

How do you convert a value to a standard score (z-score)?

• Add the mean, then multiply by the standard deviation.

• Subtract the mean, then divide by the standard deviation.

• Multiply by the mean, then add the standard deviation.

• Divide by the mean, then subtract the standard deviation.

Multiple Choice

What does a z-score of 2 indicate about the position of a data point in a normal distribution?

• The data point is 2 standard deviations above the mean

• The data point is 2 standard deviations below the mean

• The data point is at the mean

• The data point is at the median

Open Ended

Find the z-scores for x1 = 325 and x2 = 366.21. Interpret each z-score. What can you say about x1 = 325 and x2 = 366.21?

Multiple Choice

What is the empirical rule also known as?

• 68-95-99.7 rule

• 50-75-99 rule

• 60-90-100 rule

• 70-80-90 rule

Fill in the Blanks

About 68% of the y values lie between what two values? These values are _______________. The z-scores are _______________, respectively.

Multiple Choice

The shaded area in a normal distribution graph represents the probability P(X < x). What does the area to the right of the vertical line through x represent?

• P(X > x)

• P(X < x)

• P(X = x)

• P(X ≤ x)

Fill in the Blanks

Suppose a 15 to 18-year-old male from Chile was 176 cm tall from 2009 to 2010. The z-score when x = 176 cm is z = _______. This z-score tells you that x = 176 cm is _______ standard deviations to the _______ (right or left) of the mean ______ (What is the mean?).

Multiple Choice

What is the formula to find a percentile?

• Percentile = x̄ + zσ

• Percentile = x̄ - zσ

• Percentile = zσ + x̄

• Percentile = zσ - x̄

Multiple Choice

What is the z-score for the 75th percentile?

• 0.675

• 1.282

• 1.645

• 0

Open Ended

How do you calculate the 90th percentile for a given data set?

Fill in the Blanks

The normal distribution is also known as the

curve.

Open Ended

How confident do you feel about using the normal distribution curve after this session?

Multiple Choice

What is the main objective of learning about the normal distribution curve?

• To understand probability

• To use the normal distribution curve

• To learn about statistics

• To analyze data