In April 2025
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A pair of die is rolled, what is the probability of getting a 5 or a 6?
There are five cards in a box containing the numbers 1, 3, 5, 7, and 9. A sample of size 3 is
to be drawn at a time. List all possible sample size of 3 from this population and compute the
mean and variance of the sampling distribution of the sample means.
- Compute the population mean.
- Compute the population variance.
- Determine the number of possible samples.
- List all possible samples and their corresponding means.
- Construct the sampling distribution of the sample means.
- Compute the mean of the sampling distribution of the sample means.
- Compute the variance of the sampling distribution of the sample means.
- Construct the histogram.
2. A line for tickets to a local concert had an average waiting time of 20 min. and a σ = 4 min. a. What percentage of the people in line will wait for more than 28 minutes? b. If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes? c. How many minutes of waiting time would include 95% of those who would fall in line?
Suppose that the life span in months of a lead bulb is a random variable and let Y1 and Y2 denote
the life span of two different types of lead bulbs produced by different companies. If Y1 and Y2 are
independent exponentially distributed random variables, both with mean β and let X1 =
Y1
Y1 + Y2
and
X2 = Y1 + Y2. Find and identify the marginal distributions of X1 and X2.
A basket has 12 marigolds and 8 carnations. if we had picked two flowers one by one with replacement, find the probability of getting a marigold and a carnation.
On average, four students visits the Mathematics and Statistics tutoring centre during a 5-minute period.
(a) Calculate the probability that three students visit the centre during a 5 minute period. (3)
(b) During a ten-minute period, what is the probability that at least 4 students visit the centre? (5)
The mean water consumption of 10 students in a week is 28 liters with a standard deviation of 1.6 liters. Consider 95% confidence level, the upper limit is
3. In a Harris poll of 630 human resource professionals, 38.4 % said that they had at least one child by the age of 30 years.
a. Among the 630 professionals who were surveyed, how many of them said they had at least one child before 30 years of age.
b. Construct a 99% confidence interval estimate for the proportion of all human resource professionals with at least one child before 30 years of age.
c. Repeat part (b) using a confidence interval level of 90%.
d. Compare the confidence intervals from part (b) and (c) and identify the interval that is wider. Why is it wider?
4. In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the consumer electronics association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high definition television. Are the results from a few years ago likely to be valid today?
1. A random sample of 15 fence posts from a garden centre was found to have a mean length of 1.84 m. The population standard deviation for these posts is taken to be 17cm.
(i) Use the t-distribution to find a symmetric 95% confidence interval for the mean length of such posts.
(ii) Interpret the 95% confidence interval found in part (i) above.
2. A particular brand of petrol was used in 80 randomly chosen cars of the same model and age. The petrol consumption, x miles per gallon, was obtained for each car. The results are summarized by
∑x=1896 and ∑x2=45959.
Calculate a 99% confidence interval for the mean petrol consumption of all cars of this model and age.
What is probability that 12 or more boxes will be dilevered on a particular day
