Choose the <b>correct</b> answer from the options given below :-

The marks obtained by five students in a test of Applied Mathematics carrying 100 marks are 49, 58, 67, 92, 99. Then the point estimate of the population mean is

Match List-I with List-II

Choose the correct answer from the options given below:

Which of the following are true ?

(A) If the mean of a normal variate is 12 and standard deviation is 4, then the Z-score of data point 20 is 2.

(B) Mean of the numbers obtained on throwing a die having '1' on three faces, '2' on two faces and '5' on one face is 3.

(C) If the variance of a Poisson's distribution is 2, then $P(X=0)=\frac{1}{e^2}$.

(D) For a binomial distribution, mean = 9 and the standard deviation is $\frac{3}{2}$, then the number of trials is 12.

Choose the correct answer from the options given below:

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\overline{X_1}$ and $\overline{X_2}$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\overline{X_1}$ and $\overline{X_2}$ differ significantly or not, the $t$-test statistic is given by

Consider the following hypothesis test :

$H_0: \mu \le 35$

$H_a: \mu > 35$

A sample of 49 provided a sample mean of 38.2 The population standard deviation is 8. The value of test-statistic is,

The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is