Statistics and Probability Answers

Calculate the 4 point moving averages for this list of data 5,3,6,8,7,5,3,5.

Height of Australian women is normally distributed with a mean of 172 cm and a standard deviation of 8 cm. The 5% tallest Australian women would have a height at least ___ cm

A good critic is eating at a restaurant. She selects 4 items at random from the menu. If there are 22 items on the menu, what is the probability that she selects the restaurant’s four best dishes?

Mr. Roy randomly selects 2 students out of 18 to pass out papers at the start of class. What is the probability that you and your friend are chosen?

a) we write the null hypothesis (if necessary)

b) solution

c) result

d) answer (together with a comparison to the theoretical distribution, if needed)

(3 p.) Calculate the sum of the given series of numbers, arithmetic mean and average deviation, variance, standard deviation and coefficient of variation and make historgam:

1, 2, 3, 4, 5, 5.1, 5.2, 5.4, 5.6, 5.7, 5.9, 6.1, 6.4, 6.7, 7.5, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 99

(1 p.) The population density in two 100,000-people cities is 700 people / km2 and 200 people / km2, respectively. Calculate the average population density

(2 p.) Check if the exam pass rate depends on sex

pass Not pass  

W 21 5  

M 47 20  

(3 p.) Does the speed of the runner depend on the color of the shirt?

black            white Green  

4.8

4.9

4.0

4.6

5.1

5.3 4.4

4.3

4.4

4.2

4.0

4.0 3.9

5.1

4.9

4.8

4.7

4.6  

(2 p.) Check if the exam pass rate depends on the time you are studying

Time in days 1 2 3 4 5 6 7 8 9  

grade        2 2 3 3.5 4 4 5 5 5  

(2 p.) Two development companies have purchased land for housing. Already after the purchase, a questionary was conducted regarding the most fashionable areas in the city. Based on this information, check if any of these companies have better land for housing.

A  1

B  2

C  3

D  4 

E  5

F  6

G  7

H  8

I  9

J  10

companie 1: A, B, C, D, I

kompanie 2: E, F, G, H, J

Eight boys and three girls are to sit in a row for a photograph. Find the probability that no two girls are together.

To compare customer satisfaction levels of two competing ice cream companies, 8 customers of Company 1 and 5 customers of Company 2 ware randomly selected and were asked to rate their ice creams on a five-point scale, with 1 being least satisfied and 5 most satisfied. The survey results are summarized in the following table:

Company 1

𝑛1=8

𝑋1 =3.21

 𝑆1= 0.31

Company 2

𝑛2=5

𝑋2=2.22

𝑆2= 0. 21

By assuming both equal variances and unequal variances:

a. Construct an interval estimate at 95°/ confidence interval for difference of means of two ice cream companies.

The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling. 29 38 38 33 38 21 45 34 40 37 37 42 30 29 35 a. Develop a 95 percent confidence interval for the population mean. Interpret the result. 

To compare customer satisfaction levels of two competing ice cream companies, 8 customers of Company 1 and 5 customers of Company 2 ware randomly selected and were asked to rate their ice creams on a five-point scale, with 1 being least satisfied and 5 most satisfied. The survey results are summarized in the following table: Company 1 Company 2 𝑛1=8 𝑛2=5 𝑋1 ̅̅̅̅=3.21 𝑋2 ̅̅̅̅=2.22 𝑆1= 0.31 𝑆2= 0. 21 By assuming both equal variances and unequal variances: a. Construct an interval estimate at 95°/ confidence interval for difference of means of two ice cream companies.