Statistics and Probability Answers

Identify the type of variable in each case:
1. Gender 2. Education Behaviour 3. Satisfaction 4. Motivation 5. Echange Rate 6. Gold price 7. Preference of cars

In an experiment, the first sample with n1 = 10 has a standard deviation of s1 = 0.5. The second sample with n2 = 8 has a standard deviation s2 = 0.7.

Determine the 98% confidence interval for (s_1/2)/(s_2/2) which is the ratio of the population variance.

The fuel consumption of a new model of car manufactured by Kantanka Automobile Limited is being tested.In one trial, 50 cars chosen at random were driven under identical conditions and the distance ,xkm on 1liter of petrol were recorded . The results gave the following totals.
summation of x =525 , summation of x2=5625.
Calculate the 95% confidence interval for the average petrol consumption , in kilometer per liter ,of car of this type.

If u=3 and standard deviation =0.5, find P(x>4). If it's necessary to reduce this probability to 0.01,to what value must be changed;keeping standard deviation constant.

for finding the p-value when the population standard deviation is unknown if it is possible to assume that the population is normal, we use

iii. State the relation between the order of a group and the number of binary operations that can be defined on that set. How many binary operations can be defined on a set with 4 elements?

Q1 : Three missiles are fired at target .If the probability of hitting the

target are 0.4 ,0.5 , 0.6 respectively , if the missiles are fired independently , what is the probability .

(i)that all the missiles hit the target ?

(ii) that at least one of three hits the target ?

(iii) that exactly one hits the target?

(iv)that exactly 2 hit the target?

The number of pages in a PDF document you create has a discrete uniform distribution from five to nine pages (including the end points). What are the mean and standard deviation of the number of pages in the document ?

The marketing director of GH HOTEL was interested in studying the intention of consumers
to visit their facility after the president has fully lifted the restriction on public gathering in
2020 and as a follow- up, whether they in fact actually visited. Suppose that a sample of 1000
household was initially selected and the respondents were asked whether they planned to visit
GH HOTEL. Twelve months later the same respondents were asked whether they actually
visited the hotel. The results are summarized in the table below
Planned to visit Yes No Total
Yes 200 50 250
No 100 650 750
Total 300 700 1000
i. Draw a tree diagram to represent the information in the table.
ii. Find the probability of selecting a respondent who actually visited GH HOTEL.
Interpret your answer in a simple single sentence.
iii. Find the probability of panned visit or actual visit.
iv. Calculate the probability that a respondent actual

x= 3.1, 9.4, 1.2, 1.0, 9.0, 5.0, 3.4, 7.4, 0.1, 7.5
y= 8.9, 15.0, 4.8, 6.0, 14.9, 11.9, 9.8, 15.0, 4.7, 13.0

what is the coefficient of determination for this data set?