normal distribution

about __ of observations fall between μ - σ and μ + 2σ.

81.5%

15. Which of the following is not true for a standard normal (Z) distribution? a. It is symmetric. b. It has a mean of 0. c. It has a median of 0. d. The Z distribution is a discrete distribution

d

What proportion of the data from a normal distribution is within two standard deviations on either side of the mean? a. 0.3413 b. 0.4772 c. 0.6826 d. 0.9544

d

the Z-table always gives you the probability of being ___ than the number you are looking up

less

the Z distribution has a table that displays what type of probabilities: less-than or greater-than?

less-than

the Z distribution is a special distribution whose mean is __ and SD is __?

mean is 0 and SD is 1

if Z = 0, then where is X compared to its mean?

when Z=0, then X=the mean

μ is the ____ of the normal distribution and σ (called sigma) is the _____

MEAN, STANDARD DEVIATION

Suppose the Z value is -1.26. Which row and column do you look in to find P(Z<-1.26)?

Row: -1.2 Column: 0.06

suppose the z value is 2.00. which row and column do you look in to find P(Z<2.00)?

Row: 2.0 Column: 0.00

Suppose the the Z value is 2.18. Which row and column do you look in to find P(Z<2.18)?

Row: 2.1 Column: 0.08

a z-value tells you how many ___ the x value is above (or below) its __?

SDs, mean

"Between two numbers" probabilities. a. If you want the probability of being between two values, a and b, what do you do?

With a < b, P(a<Z<b)=P(Z<b)- P(Z<a).

finding approximate probabilities. A) about __ of observations fall w/in 1 SD of the mean (i.e. within μ ± σ) B) about __ of observations fall within 2 SD of the mean. (i.e. within μ ± 2σ) C) about __ of observations fall within 3 SD of the mean. (i.e. within μ ± 3σ)

a. 68 % b. 95 % c. 99.7 %

the shape of the normal distribution is: A. Symmetric B. Skewed C. Flat D. Unknown

a. Symmetric

True or false: A random variable X is normally distributed with a mean of 250 and a standard deviation of 50. Given that X = 175, its corresponding z- score is -1.50.

a. True

If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond? a. 71.76 b. 67.96 c. 61.96 d. 48.24

a.71.76

if X is ___ the mean, the Z score will be a positive number

above

the normal distribution is: a. Discrete b. Continuous

b. Continuous

True or false: If you have a z-score of Z = 0.85 that means 85% of the data lie below you

b.False - A Z = 0.85 means we are 0.85 standard deviations above the mean. Looking at the table, we see that 80.23% of the data lies below a Z = 0.85.

True or false: The 40th percentile of the standard normal (Z) distribution occurs at the number Z = 0.40.

b.False - The 40th percentile is the Z-score where 40% of the values are below it; this occurs around Z = -0.25.

True or false: A random variable X is normally distributed with a mean of 150 and a variance of 36. Given that X = 120, its corresponding z- score is 5.0

b.False - since the given X of 120 is below the mean, the Z-score should be negative

If an observation has a z-score of -1.5, how many standard deviations is it above or below the mean? A. 1.5 SD's below the mean B. 1.5 SD's above the mean C. 0.066 SD's below the mean D. 0.066 SD's above the mean

A.

if X is below the mean the Z score will be a ___ number

negative

Where is the 10th percentile of the Z distribution? A. - 1.28 B. 1.28 C. 0.10 D. 0.90

A. -1.28

If the Z-score is 1.96, and X has a normal distribution with mean 60 and standard deviation 6, what X-value corresponds to this Z-score? A. 71.76 B. 67.96 C. 48.24 D. 61.96

A. 71.76

What is the probability that a normally distributed random variable X is greater than 85 if μ X = 75 and σ X = 4? A. 2.5 B. 0.0006 C. 1 D. 0.994

B. 0.006

Suppose X has a normal distribution with mean 10 and standard deviation 2. In order for the Z-score to be equal to 0, then X must be equal to A. 0 B. 10 C. 2 D. None of these choices are correct

B. 10

The Normal distribution is an example of a _________________ Distribution. A. discrete B. continuous C. neither

B. continuous

For a normally distributed variable X with mean 40 and standard deviation 10, what is the probability that X equals exactly 30? In notation, what is P( X = 30 ) ? A. 0.242 B. 0.159 C. 0 D. 0.841

C. 0

X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that 2X will be less than 110? A. 0.159 B. 0.023 C. 0.977 D. 0.841

D.

The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given? A. 74.8 minutes B. 84.7 minutes C. 92.3 minutes D. 78.4 minutes

D. 78.4 minutes

True or false: The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. The percentage of the students which take longer than 80 minutes to complete the exam is 84.13%.

False

the z table: the number you are looking up should have __ digit(s) before the decimal point and ___ digit(s) after the decimal point

one, two

Greater than probabilities: when you need a greater-than probability, how do you use the probability from the Z table to answer the question?

we want to find P(Z>z). We can use 1- P(Z <z)