QUESTION 1

x	P(x)
0	0.05
1	0.05
2	0.05
3	0.85

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

Question 2

When dragons on planet Dathomir lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 30% of the eggs are yellow, and the rest green. Next spring, the lead scientist has permission to randomly select 42 of the dragon eggs to incubate. Consider all the possible samples of 42 dragon eggs. What is the mean (U) number of yellow eggs in samples of 42 eggs? U = (Please show your answer to 1 decimal place) What is the standard deviation (Q) in the number of yellow eggs in samples of size 42? Q = (Please show your answer to 1 decimal place)

Question 3 The television show Pretty Betty has been successful for many years. That show recently had a share of 32, meaning that among the TV sets in use, 32% were tuned to Pretty Betty. Assume that an advertiser wants to verify that 32% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Pretty Betty broadcast. Please show your answer to 4 decimal places. Find the probability that none of the households are tuned to Pretty Betty. P(none) = Find the probability that at least one household is tuned to Pretty Betty. P(at least one) = Find the probability that at most one household is tuned to Pretty Betty. P(at most one) = If at most one household is tuned to Pretty Betty, does it appear that the 32% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Pretty Betty unusual?)

• no, it is not wrong
• yes, it is wrong

Question 4

In a normal distribution, a data value located 1 standard deviations below the mean has Standard Score: z = In a normal distribution, a data value located 2.1 standard deviations above the mean has Standard Score: z = In a normal distribution, the mean has Standard Score: z =

Question 5

A variable x is normally distributed with mean 17 and standard deviation 7. Round your answers to the nearest hundredth as needed. a) Determine the z-score for x=25.

b) Determine the z-score for x=12.

c) What value of x has a z-score of 1.43?

d) What value of x has a z-score of -0.6?

e) What value of x has a z-score of 0?

Question 6

A variable x is normally distributed with mean 20 and standard deviation 4. Round your answers to the nearest hundredth as needed. a) Determine the z-score for x=23.

z =

b) Determine the z-score for x=

z =

15.c) What value of x has a z-score of 2.25?

x =

d) What value of x has a z-score of -0.8?

x =

e) What value of x has a z-score of 0?

x=

Question 7

A variable x is normally distributed with mean 20 and standard deviation 4. Round your answers to the nearest hundredth as needed. a) Determine the z-score for x=23.

z =

b) Determine the z-score for x=

z=

15.c) What value of x has a z-score of 2.25?

x=

d) What value of x has a z-score of -0.8?

x=

e) What value of x has a z-score of 0?

x=

Question 8

Recall that a normal distribution is, bell-shaped, symmetric, where the mean, median and mode are the same. Simply put, it is a data set where most values are around the mean.

Come up with a real-life data set that is normally distributed. Write at least two sentences on why your data set exhibits the characteristics of the normal distribution.

Please answer the questions sequentially. Thank you.