4. At the end of the year the employees of an institution are graded as not satisfactory, satisfactory or outstanding. Satisfactory or outstanding employees receive a bonus. The amount of bonus varies from employee to employee but calculated so that bonuses given to satisfactory employees are normally distributed with mean £1000 and standard deviation £100, for outstanding ones their bonuses are normally distributed with mean £2000 and standard deviation of £500.

I am interested in whether my partner, Paul, has been graded satisfactory or outstanding. He will not tell me but found his pay slip which shows he has been paid a bonus of £1200.

a. Write down suitable hypotheses that I wish to test.

b. Given that the Z score indicates that P>2 is 0.0228, what conclusion can be reached at 5% significance level.