If X ~ N(9,81) the standard normal variate Z will be ________.

(a)

\(Z=\frac { X- 81 }{ 9 } \)

(b)

\(Z=\frac { X-9 }{ 81 } \)

(c)

\(Z=\frac { X-9 }{ 9 } \)

(d)

\(Z=\frac { 9-X }{ 9 } \)

A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is ________.

(a)

2.5 e^-1

(b)

e^-1

(c)

2e^-1

(d)

none of the above

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to ________.

(a)

(2/3)⁶

(b)

(2/3)⁵(1/3)

(c)

(1/3)⁶

(d)

4(2/3)⁶

Which of the following cannot generate a Poisson distribution?

(a)

The number of telephone calls received in a ten-minute interval

(b)

The number of customers arriving at a petrol station

(c)

The number of bacteria found in a cubic feet of soil

(d)

The number of misprints per page

The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of  Rs.180,000 and a standard deviation of Rs. 10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs. 165,000 and Rs. 175,000 per annum?

(a)

0.819

(b)

0.242

(c)

0.286

(d)

0.533

If P(Z > z) = 0.8508 what is the value of z (z has a standard normal distribution)?

(a)

–0.48

(b)

0.48

(c)

-1.04

(d)

1.04

In a binomial distribution if the mean is 8 and the variance is 6, then the number of trials is ___________

(a)

32

(b)

48

(c)

16

(d)

12

If the mean of the binomial distribution is 25, then its standard deviation lies in the interval ___________

(a)

[0,5)

(b)

(0,5]

(c)

[0,25]

(d)

(0,25]

The variance of a binomial distribution is ___________

(a)

equal to its mean

(b)

less than its mean

(c)

greater than its mean

(d)

none

The sum of the mean and variance of a binomial distribution for 6 trial is 2.16. Then p = _______

(a)

0.4

(b)

0.6

(c)

0.8

(d)

0.2