Statistics and Probability Answers

The Center for Information and Research on Civic Learning and Engagement (CIRCLE), an independent youth research organization, reported that 49% of all U.S. adults age 18 to 29 voted in the 2012 presidential election. We believe that a higher proportion of community college students plan to vote in the 2016 presidential election.

H0: 49% of community college students plan to vote in the next presidential election.

Ha: More than 49% of community college students plan to vote in the next presidential election.

We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is approximately 0.01.

At a significance level of 0.05, what can we conclude?

The height of students in a school is normally distributed with mean 138 centimetres and standard deviation equal to 15 centimetres. What is the minimum height of a student such that P(X≥x) = 0.0548?

Question 2

(a) It is noted that 8% of Kaplan students are left handed. If 20 (TWENTY) students are randomly

selected, calculate the

i. probability that none of them are left-handed, (2 marks)

ii. probability that at most 2 are left-handed, (3 marks)

iii. standard deviation for the number of left-handed students (2 marks)

(b) If 50 (FIFTY) classes of 20 (TWENTY) students are randomly selected, what is the probability that 10

(TEN) classes have no left-handed students?

A random sample of 700 units from a large consignment showed that 200 were damaged. Find
95% confidence interval for the proportion of damaged unit in the consignment.

Free range eggs are produced on a farm. The weights of eggs are found to be normally distributed with a mean of 55g and a standard deviation of 1g. Using the empirical rule and no calculations, determine whether it is likely a randomly chosen egg from the farm would have the following weight.



a. 51g
b. 53g
c. 56g

Three groups of children consist of 3 girls and 1 boy, 2 girls and 2 boys, 1 girl and 3 boys respectively. One child is picked up at random from each group. Find the probability that the selection consist of 1 girl and 2 boys?

The probability that a randomly selected 11​-year-old male feral cat will live to be 22 years old is 0.76526. ​(a) What is the probability that two randomly selected 11​-year-old male feral cats will live to be 22 years​ old?

The construction of a building may be delayed by a strike. Suppose that the
probability that there will be a strike is 0.70, the probability that the construction
will be completed on time if there is no strike is 0.90 and the probability that the
building will be completed on time if there is a strike is 0.40, what is the
probability that the construction will be completed on time.

a) An athlete is running in four races and in each race she has a 60% chance of
winning. What is the probability that she will win at least two races?
b) A website has on the average two hits per hour. Assuming a Poisson distribution for
the number of hits per hour (X), calculate the probability that there are at most three
hits.

A committee of four is to be formed from among 5 economists, 4 engineers, 2 statisticians and 1 doctor . Find the probabilities that,
(i) Each profession is represented in the committee
(ii) Has atleast one economists
(iii) Has a doctor as a member and three others
(Iv) Has atleast one engineer but no economists