Math Answers

((xn,yn) is convergent iff both (xn}) and (yn) are convergent. In fact, for(x0 ,y0) in R2, we have (xn ,yn) converging to (x0,y0) iff xn converges to x0 and yn converges to y0

In the mid-1990s, time magazine reported that 27% of the US Congress supported a tax cut as a means of stimulating the economy and increasing Tax revenues. Suppose at that time five members of congress were randomly selected for an interview and asked whether they supported the tax cut to stimulate the economy.

Find the probability that:

2.1 At least three of the five members were in favour of a tax cut. (6)

2.2 Less than five members were in favour of a tax cut. (6)

2.3 Not more than 3 members were in favour of the tax. (6)

2.4 Find the mean of the above distribution (6)

2.5 Find the variance and standard deviation of the above distribution (6)

what is the probability that at least five out of 20 young executives practice good reading habits

The following data are the measures of the diameters of 36 rivet heads in 1/100 of an inch.

6.72 6.77 6.82 6.70 6.78 6.70 6.62 6.75

6.66 6.66 6.64 6.76 6.73 6.80 6.72 6.76

6.76 6.68 6.66 6.62 6.72 6.76 6.70 6.78

6.76 6.67 6.70 6.72 6.74 6.81 6.79 6.78

6.66 6.76 6.76 6.72

Compute the Arithmetic Mean, variance, standard deviation, Coecient of Variation, Coe-

cient of Skewness and Coecient of Kurtosis..

The weights of students in a certain school are normally distributed with a mean weight of 66 kg. 10% have a weight greater than 70kg. What percentage of students weighs between 62kg and 66kg?

A random sample of 11 observations was taken from normal population. The sample mean and standard deviation are 74.5 and 9 accordingly. Can we infer at 5% significance level that the population mean is greater than 70?

A random of 25 observations was drawn from a normal population. The sample mean and the sample standard deviation are 52 and 15 accordingly. Is there enough evidence at 10% significance level to infer that the population mean is not equal to 50? Estimate the population mean as well.

A 100-volt electromotive force is applied to an RC series circuit in which the resistance is 200 ohms and the capacitance is 10−4 farad. Find the charge q(t) on the capacitor if q(0) = 0. Find the current i(t).

Pamela borrows an amount of money for emergency house repairs. The interest on the loan is compounded

quarterly. After four years the debt accumulated by R7 980,00 to the amount of R32 923,00. The yearly

interest rate, expressed as a percentage and rounded to two decimal places, at which the money was borrowed,

is

[1] 1,75%.

[2] 8,00%.

[3] 9,26%.

[4] 7,00%

An amount of money is invested at 8% interest per year, compounded quarterly. After a number of years, the

accumulated amount in the account is R7 365,00. The investment earned R2 000,00 interest in this period.

If the accumulated amount is left in the account (the interest rate remains the same) for another period that

is one year longer than the first period, the accumulated amount in the account will then be

[1] R10 312,78

[2] R29 363,56

[3] R10 944,00

[4] R10 699,8