A petrol station finds that its daily sales, in litres, are normally distributed with mean $4520$ and standard deviation $560$. Find on how many days of the year ($365$ days) the daily sales can be expected to exceed $3900$ litres.

(Write answer nearest to whole number)

The daily sales at petrol station are $X$ litres, where $X$ is normally distributed with mean $m$ and standard deviation $560$. It is given that $P\left(X>8000\right)=0.122$.

Find the value of $m$.

(Round answer up to $1$ decimal place)

Find the probability that daily sales at this petrol station exceed $8000$ litres on fewer than $2$ of $6$ randomly chosen days.

(Write answer up to $4$ decimal places)

(Write answer up to $2$ decimal places)

The weights, $X$ grams, of bars of soap are normally distributed with mean $125$ grams and standard deviation $4.2$ grams.

Find the probability that a randomly chosen bar of soap weighs more than $128$ grams.

The weights, $X$ grams, of bars of soap are normally distributed with mean $125$ grams and standard deviation $4.2$ grams.

Find the value of $k$ such that $P\left(k<X<128\right)=0.7465.$ Use $\left[\varphi \left(0.714\right)=0.7627, {\varphi }^{-1}\left(0.0162\right)=-2.14\right]$