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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The probability that a person over 60 years of age in a certain community drinks alcohol 2/5 is
and the probability that a person over 60 years of age has heart disease is 2/15 . The
probability that a person over 60 years of age drinks alcohol and has heart disease is 1/16 . Are
‘drinking alcohol’ and ‘heart disease’ independent events?
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 ?
If p is the length of the perpendicular from the origin to the line x/a + y/b = 1 prove that 1/p2 = 1/a2 + 1/b2.
Determine the value of the constant a if the function f (x) defined below is continuous at x = 2.
Find the probability of drawing an ace or a spade from a deck of 52 cards in a single draw.
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.
for a population of size N = 120 with a mean of 7.5 and a standard deviation of 1.5, find the estimated standard error of the mean for the following sample sizes:
- ) n = 9 ii) n = 25