The time $x(min)$ for a laboratory assistant to prepare the equipment for a certain

experiment is to have a uniform distribution with $A=25$ and $B=35.$

$($a$)$ What is the probability that probability time exceeds $33$min $?$

$[2$ marks$]$

$($b$)$ What is the probability that preparation time is within $2$min of the mean time?

$[2$ marks$]$

A geologist has collected $10$ specimens of basaltic rock and $10$ specimens of granite. The

geologist instructs a laboratory assistant to randomly select $15(x)$ of the specimens for

analysis.

$($a$)$ What is the probability that five specimens of basaltic rock are selected for analysis?

$[2$ marks$]$

$($b$)$ What is the probability that the number of granite specimens selected for analysis

is within $1$ standard deviation of its mean value?

$[4$ marks$]$

A sequence of independent tosses was made with a coin for which the probability of

obtaining a head on any given toss is $\frac{1}{30}.$

$($a$)$ What is the expected number of tails that will be required in order to obtain before

five $($Y$)$ heads have been obtained?

$[2$ marks$]$

$($b$)$ What is the variance of the number of tails that will be obtained before five heads

have been obtained?

$[2$ marks$]$