Discuss the below:
Q1. Calculate the mean, median and standard deviation of the following data:
10, 16, 12, 20, 18, 209, 16, 11, 13, 14, 17, 20, 25
Q2. Prepare a relative frequency histogram of the following data, use 4 classes.
43, 35, 41, 41, 39, 38, 41, 40, 45, 43, 52, 36, 43, 38, 39, 44, 45, 30, 37, 40, 39, 41, 44, 46, 39, 40, 44, 37, 47, 48, 49, 51, 53, 52, 51, 39.
Q3. Calculate the probability of the following binomial distributions.
(a). P (X = 1) if n = 11 and p = 0.26
(b). P (X > 2) if n = 12, p = 0.42
Q4. For a Poisson distribution with mean 3, calculate the following probabilities.
(a). P {X < 4}
(b). P {X = 5}
Q5. Calculate the expected value and the variance of the random variable X having the following probabilities
X 20 25 30 40 50 60
P (X) 0.1 0.25 0.1 0.25 0.16 0.14
Q6. Suppose that a random variable X is distributed as normal with mean 100 and variance 9. Calculate the following probabilities.
(a). P (X > 105) (b). P (99 < X < 103)
Q7. Calculate 95% confidence interval for µ if X‾= 25, s2 = 6 and n = 24. Assume the observations are from a normal population.