The monthly production of units in a factory is normally distributed with mean $\mu$ and standard deviation $\sigma$. Their $Z$-scores corresponding to the production of $2400$ units and $1800$ units are $1$ and $-0.5$ respectively. Find its mean and standard deviation.
The mean and variance of a binomial distribution arc $3.4$ and $2.73$ respectively. Find the number of Bemoulli trials conducted in this distribution and write $p ( x )$. OR State properties of binomial distribution. $($Any four$)$
Determine the value of the Correlation coefficient from the following results. $\operatorname{cov}(x, y): S=3: 5 \text { and } S_x: S_y=1: 2 \text {. }$
The wholesale price index numbers for the year $2015$ and $2016$ are found to be $177.6$ and $181.2$ respectively. Find the rate of inflation using index numbers of both the years.