Practise modelling continuous measurements with a normal curve, shading probability regions and using symmetry or standard-normal tables for intervals measured from the mean.
The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg . On 10 % of days less than 16 kg of grapes are sold.
In a random sample of 365 days, on how many days would you expect the mass of grapes sold to be within 1.3 standard deviations of the mean?
The probability of being within 1.3 standard deviations of the mean is
P(−1.3<Z<1.3)=2Φ(1.3)−1=2(0.9032)−1=0.8064.
In 365 days, the expected number is
365(0.8064)=294.3,
so the answer is 294 days.