Statistics and Probability Answers

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whole question in photo,B=4,you can sub B=4

Tests Involving Means and Proportions

Problem:
A sample survey of 500 students, 300 from the first year level and 200 from the second year level, showed that 56% and 48%, respectively, were in favor of using Google Classroom for the delivery of online classes. At a level of significance of 0.05, test the hypothesis that
(a) there is a difference between the two year levels
(b) Google Classroom is preferred by the first year students
(c) Find the P values in tests (a) and (b)

MMA tests the hypothesis that the average nbr of FNP is more than 4. Consider this to help carry out the test. n=30, x̅=5.5, σ=3 and a=0.01. Answer Q 12 to 16

Q 12
The correct set of hypothesis is
1. Ho : μ = 4; H1 : μ ≠ 4
2. Ho : μ = 5.5; H1 : μ ≠ 5.5
3. Ho : μ = 4; H1 : μ > 4
4. Ho : μ = 5.5; H1 : μ > 5.5
5. Ho : X = 4; H1 : X > 4

Q 13
The applicable test statistic is
1. Z test
2. t test
3. Chi–Square test
4. F–test

Q 14
The value of the test statistic and the critical value are
1. 1.5 and 2.33
2. 2.74 and 2.33
3. 2.74 and 2.58
4. 1.5 and 2.58

Q 15
The p-value for the test is
1. 0.0062
2. 0.0668
3. 0.1336
4. 0.0031

Q 16
What decision and conclusion can we take with regard to the hypothesis test
1. Reject null hypothesis(NH) and conclude that the average nbr of FNP > 4
2. Reject NH and conclude that the average nbr of FNP = 4
3. Don't eject NH and conclude that the average nbr of FNP = 4
4. Accept the NH

A baseball team has scheduled it's opening game for April 1. It is assumed that if it snows on April 1, the game is postponed and will be played on the next day that it does not snow. The team purchased insurance against snow. The policy will pay USD 1,000 for each day, up to 2 days that the game is postponed.
It is determined that the number of consecutive days of snow beginning on April 1, is a Poisson random variable with
mean 0.6.
What is the standard deviation of the amount that the insurance company
will have to pay.

Let X be a continuous r.v with density function f(x) =  |x| 10 0, . Calculate the expected value of X

A recent study shows that the annual cost of maintaining a building in Texas averages
200 US Dollars with a variance of 260 US Dollars. If a tax of 30% is introduced on all items
associated with the maintenance of building i.e. everything is made 30% more expensive.
Calculate the standard deviation of the annual cost of maintaining a building in Texas.

A company prices its hurricane insurance using the following assumptions:
i. In any calendar year, there can be at most one hurricane.
ii. In any calendar year, the probability of a hurricane is 0.05 .
iii. The number of hurricanes in any calendar year is independent of the number of
hurricanes in any other calendar year.
Using the company’s assumptions, calculate the probability that there are fewer than
3 hurricanes in a 20-year period.

A financial analyst has found out that policyholders are four times as likely to file two
claims as to file four claims. If the number of claims filed has a poisson distribution,
What is the variance of the number of claims filed.

Suppose an airline accepted 12 reservations for a commuter plane with 10 seats. They
know that 7 reservations went to regular commuters who will show up for sure. The
other 5 passengers will show up with a 50% chance, independently of each other.
(a) Find the probability that the flight will be overbooked.
(b) Find the probability that there will be empty seats.

Question 5:
A box contains 4 bad and 6 good bulbs. Two are selected randomly. One of them is tested and found good. What is the probability that other will be good too?
“A” student in a class can solve 75% of the problems and another student “B” can solve 70%. What is the probability either A or B can solve a problem if chosen at random?

Question 6:
Let A and B are two events such that P(A)= ¼, P(A/B)=1/2, P(B/A)=2/3
Let A and B are independent events
A & B are mutually exclusive events.
Find P(A∩B) and P(B)

Question 7:
Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head?

Question 8:
Two fair dice, one red and one green, are thrown. Let A denote the event that the red die shows an even number and B, the event the green die shows 5 or 6. Show that event A & B are independent.
[hint: you may take help from last file of probability handouts there mentioned formulas of dependent/independent events]