Question 1

Using the distribution in the previous question, calculate z scores for: 
a. X = 11 
b. X = 35 
c. X = 71

Accepted Answer

The answer of Using the distribution in the previous question,...

Question 2

Most statistical techniques are based on the assumption that the population of observations is not normal.

Accepted Answer

Most statistical techniques are actually based on the assumption that the population of observations is normal. If the population is not normal, some techniques may still be applied if certain conditions are met or if transformations are made to the data.

Question 3

Create a z distribution based on the following data. Explain the process. 
10 20 20 30 30 30 40 40 40 40 50 50 50 60 60 70

Accepted Answer

The answer of Create a z distribution based on the...

Question 4

A z score refers to the number of standard deviations above or below the mode.

Accepted Answer

A z score refers to the number of standard deviations above or below the mean, not the mode.

Question 5

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Accepted Answer

This is the definition of the standard normal distribution.

Question 6

The normal distribution is bimodal and symmetric.

Accepted Answer

The normal distribution is unimodal and symmetric. It has one peak and is symmetrical around its mean value.

Question 7

The basketball team lives in another dorm from those in the previous question. Their heights are normally distributed as well, with a mean height of 71 inches and a standard deviation of 2 inches. 
a. Draw their distribution on the same graph as students who lived in the first dorm (e.g., draw separate but overlapping distributions). 
b. What percent of students in the first dorm are at least as tall as the average basketball players? 
c. What percent of basketball players are taller than the average dorm resident?

Accepted Answer

The answer of The basketball team lives in another dorm...

Question 8

Based on the previous data, we could conclude that 90% of the students are likely to fall between what heights?

Accepted Answer

The answer of Based on the previous data, we could...

Question 9

Based on the height data in the previous question: 
a. What percent of residents are between 65 inches and 71 inches tall? 
b. What percent of residents are taller than 72 inches? 
c. What percent of residents are shorter than 72 inches?

Accepted Answer

The answer of Based on the height data in the...

Question 10

The area under a particular portion of the normal curve is equivalent to theprobability of falling within that portion of the distribution.

Accepted Answer

This statement is true. The area under the normal curve represents the proportion of observations that fall within that portion of the distribution.

Question 11

The probability that a student will score between plus or minus one standard deviation from the mean on an exam, assuming the scores are normally distributed, is approximately 68%.

Accepted Answer

This statement is true according to the empirical rule (also known as the 68-95-99.7 rule) for normal distributions. The rule states that approximately 68% of the data falls within one standard deviation of the mean.

Question 12

The birth weight of healthy, full term infants in the United States is nearly normally distributed. The mean weight is 3,500 grams, and the standard deviation is 500 grams. 
  
a. What percent of healthy newborns will weigh more than 3,250 grams? 
b. What weights would 95% of all healthy newborns tend to fall between? 
c. What is the z score for an infant who weighs 2,750 grams? 
​

Accepted Answer

The answer of The birth weight of healthy, full term...

Question 13

In a normal distribution, indicate what percent of scores fall: 
a. between the mean and 1 standard deviation above the mean 
b. between plus and minus 2 standard deviations of the mean. 
c. 3 standard deviations above or below the mean.

Accepted Answer

The answer of In a normal distribution, indicate what percent...

Question 14

In a normal distribution, the majority of scores fall beyond plus or minus one standard deviation from the mean.

Accepted Answer

In a normal distribution, about 68% of scores fall within plus or minus one standard deviation from the mean, indicating the majority of scores are within this range, not beyond it.

Question 15

At a neighboring university, the average salary is also $45,000 and the distribution is normal. If $47,000 has a z score of 1.5, what is the standard deviation?

Accepted Answer

The answer of At a neighboring university, the average salary...

Question 16

If the salary of assistant professors in this university is normally distributed with a mean of $45,000 and a standard deviation of $1,500, what salary would have a z score of .97?

Accepted Answer

The answer of If the salary of assistant professors in...

Question 17

The height of students in a dormitory is normally distributed with a mean of 68 inches and a standard deviation of 3 inches. Draw the distribution.

Accepted Answer

The answer of The height of students in a dormitory...

Question 18

Performing a linear transformation can make any distribution normal.

Accepted Answer

Performing a linear transformation cannot make any distribution normal. In some cases, it can approximate a normal distribution or transform a non-normal distribution to a different non-normal distribution. However, there are certain distributions that cannot be transformed into a normal distribution through linear transformations.

Question 19

Suzie scored in the 95^th percentile on the Math portion of the SAT. This means that she scored as high or higher than 95% of the other students who took the test.

Accepted Answer

The statement correctly describes what it means to score in the 95th percentile on a standardized test.

Quiz 6: The Normal Distribution

Using the distribution in the previous question, calculate z scores for: a. X = 11 b. X = 35 c. X = 71