Statistics and Probability Answers

The random variable X represents the number of heads that occur when you toss 4 coins at the same time what is the probability distribution

A Store-It-All storage facility requires users to enter a four digit code, using numbers 0-9, to get through the gate. You need to get a box of winter clothes from your storage container, but you forgot the code. 

1. If the digits can be repeated, how many possible codes are there?

There are _____ different codes. 

Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $2.

A study has been conducted on the management of 100 homestay operators nationwide.

The study focuses on the factors influencing homestay operators’ income. The

regression results from the multiple regression estimate is as follows.

Model Summary

b

R Square Adjusted R Square Std. Error of the Estimate

- 0.4952 5.512

ANOVA

a

Sum of Squares df Mean Square F

Regression 3132.80 6 522.13 17.19

Residual 2825.60 93 30.38

Total 5958.40 99

Coefficients

a

Unstandardized Coefficients

t Sig.

B Std. Error

Constant 38.14 6.99 5.46 0.000

X1 -0.0076 0.0013 -5.85 0.000

X2 1.65 0.63 2.62 0.011

X3 0.020 0.003 6.67 0.000

X4 0.21 0.13 1.62 0.116

X5 0.41 0.14 2.93 0.004

X6 -0.23 0.18 -1.28 0.211

Predictors: Constant, X1: number of homestay within 1 km, X2: proximity to other

homestay, X3: homestay size area, X4: number of residents around homestay, X5:

median income of residents close to the homestay, X6: distance between the homestay

and the city.

Dependent Variable: monthly income , Y

Multiple linear regression is as follows:

          0 1 1 2 2 3 3 4 4 5 5 6 6 Y X X X X X X

EPPD2023

Student No.

7

Based on the above information,

(i) Write the estimated regression equation.

(2 marks)

(ii) Test for goodness of fit of the regression model at 5% significant level.

(4 marks)

(iii) Calculate R2 and explain the meaning.

(3 marks)

EPPD2023

Student No.

8

(iv) Using  = 0.01, do factors affecting the income of the homestay operators are statistically significant? Explain.

(6 marks)

GOOD

Four coins are tossed. Let Y be the random variable that represents the number tail that will occur. Find the values of random variable Y.

Aerospace industry believes that the cost of a space project is a function of the weight of the major object being space sent into space. The following data represent weight in tons and the cost in $ millions.

Weights cost

1.59 54

3.20 150

0.56 20

0.89 25

1.45 40

1.90 120

2.57 124

calculate:

1) construct regression equation

2) What is the strength of the regression equation?

At a burger joint, the hourly demand of burgers show the following probability distribution. find the expected value of hourly demand and the standard deviation in hourly demand.

Number of burgers Probability

per hours

25 0.10

40 0.20

35 0.25

45 0.30

50 0.10

55 0.05

Draw all possible simples of size 2 with replacement from 3,5,7,8,9.And verify the rezult.

A random sample of 400 tins of vegetable oil, labelled ""15 kgs net weight"' gave a mean weight of 14.25 kgs with a standard deviation of 1.50 kg. Do we reject the hypothesis of net weight of 15 kgs per tin on the basis of this sample, at 5% level of significance?

Four coins are tossed. Let Z be the random variable representing the number of the heads that occur. Construct a table of the possible outcomes with corresponding values of the random variable.