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There are 60 science students tn a



Secondary School. 35 of whom study



Chemistry and 30 study Technical



Drawing, 12 out of those students atudy



Biology and chemistry but not Technical



Drawing, 10 study Chemistry but



neither biology nor Technical Drawing 11




study only Technical Drawing and



neither Biology nor Chemistry, 10 also



study Chemistry and Technical Drawing



only




a. How many mdents study all the three



subjects?



b. How many students study biology and



Technical Drawing but not Chemistry?



C. How many students study Biology only?



d How many students study biology all



together.

Show your solution:


1. If the population of ABM students of Malaya Integrated High School has a mean of 12.45, what

is the mean of the sampling distribution of its mean?

2. If the mean of the sampling distribution is 24.29, what is the mean of the population?

3. If a population of HUMS students of Makabayan National High School has a variance of 6.4,

what is the variance of the sampling distribution of the sample mean if the sample size is 4 and all

the possible samples are drawn with replacements?

4. If the population of STEM students of Siyensiya Stand Alone Senior High School has a standard

deviation of 9.4, what is the standard deviation of the sampling distribution of its means? The

sampling distribution was derived with sample size n=3, and all the possible samples were drawn

with replacements.

5. If the population standard deviation is 5.6, what is the population variance


if the base X of the right triangle shown is increasing at the rate of 3 inches per second and the height Y is decreasing at the rate of 2 inches per second, find the rate of change of the area of the triangle when X = 5 inches and Y = 7 inches. Label the units on your answer


Show that for x is greater than 1 ln x is less than or equal to 2(root x minus 1). Hence deduce that n is greater than 1 lim ln x/x raised to the power n is equal to 0




expand (1+x)^-2 using binomial theorem


Suppose a random variable  x is best described by a normal distribution with  μ = 60 and   Find the  z-score that corresponds to the value  x = 63.


Suppose a random variable x is best described by a normal distribution with μ = 60 and Find the z-score that corresponds to the value x = 63.


Let us consider two sections: section 1 contains 7 male and 10 female students, and section 2 contains 9 male and 7 female students. One section is selected at random and then one student is selected from this section. Find the probability that the selected student is male.


Given the following data on the ages of 75 persons in years. Calculate the first four central moments. Age 09.5–14.5 ,14.5–19.5 , 19.5–24.5 , 24.5–29.5 , 29.5–34.5 ,34.5–39.5, 39.5–44.5 , 44.5–49.5

Number of persons: 3,6,8,12,8,6,3,2 Total 75

Full details explain


Mabel borrowed an amount of money from her father. The loan will be paid back by means of payments of R25 000 each every second month for six years. An interest rate of 7,5% per year, compounded every two months, will be applicable. The amount of the loan is

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