Statistics and Probability Answers

One-tailed test; variance is known, α = 0.05, n = 35 

There is a bag filled with 5 blue and 4 red marbles.

A marble is taken at random from the bag, the colour is noted and then it is replaced.

Another marble is taken at random.

What is the probability of getting at least 1 blue?

A fair spinner has 9 equal sections 3 red 2 blue 4 green it is span twice what’s the probability of getting blue both times.

1.    A country town installs 2000 new electric lights in a new housing estate. These lamps have an average life of 1000 hours with a standard deviation of 200 hours. Hint: Draw and label a normal “bell-shaped” curve to help answer this?

a)   What percentage of bulbs would be expected to fail between 800 hours and 1200 hours?

b)   How many bulbs would this be?

c) How many bulbs would be expected to last longer than 1600 hours

Suppose a researcher determined that 49.3

49.3% of people 18–34 years old in the United States are men. She also finds that, among all Americans 18–34 years old, 17.1

17.1% are men and live at home with their parents, whereas 14.9

14.9% are women and live at home with their parents.

Label each branch of the following tree diagram with the correct probability value.

Suppose you just purchased a digital music player and have put 10 tracks on it. After listening to them you decide that you like 4 of the songs. With the random feature on your​ player, each of the 10 songs is played once in random order. Find the probability that among the first two songs played

​(a) You like both of them. Would this be​ unusual?

​(b) You like neither of them.

​(c) You like exactly one of them.

​(d) Redo​ (a)-(c) if a song can be replayed before all 10 songs are played.

Consider the following regression of wages (w) on the mean years of schooling of 

workers (s) and the female share in an occupation (p):

𝑙𝑜𝑔𝑤 = 0.924 + 0.150𝑠 − 0.003𝑝

 (0.154) (0.011) (0.0001)

a) Interpret the regression coefficients carefully.

b) How much variations in wages can be explained by the two regressors?

c) Would you reject the hypothesis that workers’ mean years of schooling has no 

influences on wages across professions?

 Comparable number of bedrooms and house size effects Given the, the prediction equation between y = selling price and x1 = house size and x2 = number of bedrooms was yn = 60,102 + 63.0x1 + 15,170x2.

a. For fixed number of bedrooms, how much is the house selling price predicted to increase for each square foot increase in house size? Why?

b. For a fixed house size of 2000 square feet, how does the predicted selling price change for two, three, and

four bedrooms?

Table 4 shows the selling price of three different brands of sanitizer at based on 4 randomly selected 

supermarkets. At 80% confidence level, can we conclude there is a significant difference in mean

price of the three brands of sanitizer? Make your conclusion using the p- value approach, with the aid 

of Mic. Office EXCEL.

Table 4

Brand A (in RM) Brand B (in RM) Brand C (in RM)

10.00 12.00 9.80

9.50 11.50 10.40

10.00 10.40 10.30

11.10 11.00 10.80

An electronic system has four components labeled as 1, 2, 3, and 4. The system has to be used during a given time period. The probability that component i will fail during that time period is fi for i = 1, . . . , 4. Failures of the components are physically independent of each other. A system failure occurs if component 1 fails or if at least two of the other components fail. Specify an appropriate sample space and determine the probability of a system failure.