Question

A) Fill in the blanks. (Enter an exact positive number as an integer, fraction, or decimal.)

In a normal distribution,

x = 3 and z = −1.19. This tells you that x = 3 is ________ standard deviations to the _____ (left or right) of the mean

B) Fill in the blanks. (Enter an exact positive number as an integer, fraction, or decimal.)

In a normal distribution,

x = −2 and z = 6. This tells you that x = −2 is ______standard deviations to the _____ (left or right) of the mean

C) Fill in the blanks. (Enter an exact positive number as an integer, fraction, or decimal.)

In a normal distribution,

x = 9 and z = −1.4. This tells you that x = 9 is ______standard deviations to the _____ (left or right) of the mean

D) About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution? (Enter an exact number as an integer, fraction, or decimal.)

E) About what percent of x values lie between the mean and one standard deviation (one sided)? (Enter an exact number as an integer, fraction, or decimal.)

F) About what percent of x values lie between the first and third standard deviations (both sides)? (Enter an exact number as an integer, fraction, or decimal.)

G) If the area to the left of x in a normal distribution is 0.163, what is the area to the right of x? (Enter an exact number as an integer, fraction, or decimal.)

H) Use the following information to answer the next exercise.

X ~ N(54, 8)

Find the 90^th percentile. (Round your answer to two decimal places.)

I) Find the probability that x is between four and 12. (Round your answer to four decimal places.)

X ~ N(5, 3)

Answer 1

A) Fill in the blanks.

In a normal distribution,

x = 3 and z = −1.19. This tells you that x = 3 is 1.19 standard deviations to the left of the mean

B) Fill in the blanks.

In a normal distribution,

x = −2 and z = 6. This tells you that x = −2 is 6 standard deviations to the right of the mean

C) Fill in the blanks.

In a normal distribution,

x = 9 and z = −1.4. This tells you that x = 9 is 1.4 standard deviations to the left of the mean

D) About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?

95%

E) About what percent of x values lie between the mean and one standard deviation (one sided)?

34%

F) About what percent of x values lie between the first and third standard deviations (both sides)?

31.7%

G) If the area to the left of x in a normal distribution is 0.163, what is the area to the right of x?

0.837

H) Use the following information to answer the next exercise.

X ~ N(54, 8)

Find the 90^th percentile.

64.24

I) Find the probability that x is between four and 12. (Round your answer to four decimal places.)

X ~ N(5, 3)

0.6194