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The heights of the population of boys are normally distributed with a mean of 66 inches and a
standard deviation of 8.9 inches. If a random sample of 40 boys is drawn from this population,
the barangay captain wants to conduct a study to estimate average playing time of children ages 7 to 12 he wants to be 99% confident that the sample mean will be within 15 minutes of the true mean. If he can approximate a population standard deviation by 40 minutes and assume an approximately normal distribution, how large a sample should he get?
the aptitude test was administered to random sample of 120 shs students. the sample mean was 104.2 with standard deviation of 12. find 99%confidence interval
2. A random sample of n=25 measurements is selected from a population with mean μ = 3 and standard deviation = 1. What is the probability that
a. The sample mean is greater than or equal to 3.1?
b. The sample mean is greater to 2.8, but less than or equal to3.2?
Determine the required probabilities.
Suppose you are to draw a ball from a box consisting of 2 red, 2 blue and 2 yellow balls twice.Let R be the random variable representing the number of Red. What is the probability of getting atleast 1 red?
consider tje population consisting of the value 1,3,4 list all the possible size2 that can be drawn from the population with replacement , compute the mean, variance and standard deviation of the sampling distribution of the means , construct the probability histogram of the sample mean with replacement when n=2
The table below shows data collected in a research on the relationship
between monthly income and monthly expenditure of citizens in town Q.
Use it to answer the following questions.
Earner A B C D E F G H I J
Income usd . 44 65 50 57 96 94 110 34 79 65
Expenditure usd.“ 41 60 40 50 80 68 84 30 55 48
(a) Fit the regression line of expenditure on income using least squares
method.
(b) Using the regression line obtained in (a) above, estimate the expected
amount of expenditure of a Kenyan whose monthly income is usd.
75,000.
The following distribution gives the pattern of overtime work done by
employees of a company. Calculate:
Overtime(Hours): 10-15 15-20 20-25 25-30 30-35 35-40
Number of Employees : 11 20 35 20 8 6
(a) The geometric mean
(b) The mode of the distribution
(c) Harmonic mean
(d) Variance of the distribution
(e) Obtain the Karl Pearson’s coefficient of skewness and comment on
the results.
(f) Obtain the moment-coefficient of Kurtosis of the overtime data and
interpret the results.
For a group of 20 items, sum of X = 1452, sum of x 2 = 144800 and mode = 67,
find the Karl Pearson’s coefficient of skewness and interpret the results.
2. A trader has 62 % chance of making a sale to each client. Given that the
behavior of successive clients is independent find the probability that the
trader will make a sale if two clients Lynn and Faith enter the trader’s
premises.
