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The following population is provided:17, 15, 8, 9, 7, 9, 11, 12, 14, 16, 9, 5, 10, 14, 13, 12, 12, 11, 9, 14, 8, 14, 12. Further, a simple random sample from this population gives the following values: 12, 9, 5, 10, 14, 11. Compute the sampling error for the sample mean.
a. 1.811 b. 1.167 c. 1.181 d. 1.348 e. None of the above
Thirty people, who are of the same age and the same health status, are
insured with the same insurance company. Using life tables, the company
estimates that the probability for a randomly chosen person among these 30
to be alive in 15 years from now is 0:8.
(i) What is the probability that not all 30 people will be alive in 15 years time?
(ii) What is the probability that at least one person will be alive?
The probability that a car is stolen when it is parked overnight in an unsafe
area of a city is 10%. If there are 12 cars parked on a particular street of that
area, what is the probability that during a night
(i) no car is stolen?
(ii) at most two cars are stolen?
(iii) at least nine cars are stolen?
A TV manufacturer claims that the life span of its regular TV sets is longer than 10 years with a standard deviation of 1.5 years. Using a random sample of their 16 TV sets, the average life span is found to be 11.5 years. Test the hypothesis that the TV sets' life span is longer than 10 years at a = 0.01.
A chemical company alleged that the average weight of its bag of chemical is 50 kgs. with a standard deviation of 0.9 kg. A sample of 29 bags was taken and revealed a mean weight of 48.1 kgs. Shall we accept the allegation of the chemical company? Use a = 0.01.
In a public senior high school, a survey conducted last year showed that 25%
of the students’ parents are farmers. This year, a new survey was conducted
randomly on 150 students from the same school. It was found that 63 of them
have parents who are farmers. Test if the claim was higher at α = 0.01 level.
eric wants to know if cooperative grouping is an effective strategy in improving the mathematics performance of grade 11 students. Twenty students were included in the experimental group while another 20 students were included in the controlled group. The mean achievement score of the students in the experimental group was 82.5 with a standard deviation of 3 while the mean of the students in the control group was 80 with a standards deviation of 6. the two groups come from normally distributed population. the confidence level adopted was 95%.
If P (A|B) = 0.5, P (A) = 0.45 and P (B) = ?
Let Q, and R be joint distributed random variables having joint probability density function f(Q, R) = { 1 /8 e ^−(8Q+R) , Q, R > 0
0, elsewhere
Find the probability density function of Y = 0.5(Q + R ) The joint probability density function of two random variables X1 and X2 is given by f(x1, x2) = { 8, 0 < x1 < x2 < 1
0, elsewhere
Let S = X1/x2 and V = x2 , using the change of variable technique find the joint probability density function of S and V
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#340153 on Dec 2023