The daily percentage change in the value of a company's shares is expected to be normally distributed with mean $0$ and standard deviation $0.51.$ On how many of the next $365$ working days should the company expect the value of its shares to fall by more than $1\%?$ [ Use $\Phi (1.961)=0.9751$]

Colleen exercises at home every day. The length of time she does this is normally distributed with mean $12.8$ minutes and standard deviation $\sigma .$ She exercises for more than $15$ minutes on $42$ days in a year of $365$ days.

Calculate the value of $\sigma .$[Use ${\Phi }^{-1}(0.885)=1.2$]

Colleen exercises at home every day. The length of time she does this is normally distributed with mean $12.8$ minutes and standard deviation $\sigma .$ She exercises for more than $15$ minutes on $42$ days in a year of $365$ days.

On how many days in a year would you expect Colleen to exercise for less than $10$ minutes?

The times taken by $15$ -year-olds to solve a certain puzzle are normally distributed with mean $\mu$ and standard deviation $7.42$ minutes.

Find the value of $\mu ,$ given that three-quarters of all $15$ -year-olds take over $20$ minutes to solve the puzzle.[Use ${\Phi }^{-1}(0.75)=0.674$]

The times taken by $15$ -year-olds to solve a certain puzzle are normally distributed with mean $\mu$ and standard deviation $7.42$ minutes.

Find the value of $\mu ,$ given that three-quarters of all $15$ -year-olds take over $20$ minutes to solve the puzzle.