The following distribution gives the top speeds (in kilometers per hour)
at which thirty races were clocked in auto race.
| Top speed | 145 | 150 | 160 | 170 |
| No. of racers | 9 | 8 | 11 | 2 |
Find the mean and variance of the distribution of the top speeds.
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Determine the value of the constant a if the function f (x) defined below is continuous at x = 2.
For the following set of data
95 76 72 67 69 48 37 76 74 60
78 80 48 86 59 68 73 77 51 82
94 95 48 58 75 69 55 51 89 91
89 93 69 81 68 49 86 74 79 100
i) construct a frequency distribution using intervals 35-44 etc.
ii) compute the sample mean from the raw data.
iii) compute the sample mean from the frequency distribution.
Find the probability of drawing an ace or a spade from a deck of 52 cards in a single draw.
A farmer has 200 metres of fencing with which he wishes to enclose a rectangular field. One side of the field can make use of a fence that already exists. What is the maximum area he can enclose?
Suppose that the temperature is normally distributed with expectation 50o C and variance 4o C . What is the probability that the temperature T will be between 48o C and 53o C ?
What is the probability that T ≥ 52o C ?
Find the values of x for which the function
f ( x) = x 2 − 2x + 1
is increasing or decreasing. Sketch the graph of y = f (x) .
Which of the following statements are true? Give reasons for your answers.
i) The derivative of the quotient of two functions is equal to the quotient of the derivatives of the two functions.
ii) The function of f ( x) = sin x/2 + sinx has a maxima at x = π/2 .
iii) 2x + 3 y + 4z = 0 represents a line in 3-dimenisonal space.
v) In a Binomial distribution if mean is known then standard deviation is also known.
v) If two events are mutually exclusive then they are independent.