Binomial and Normal

[2 marks]

SpeedWay airline flies from city to city . The flight time is normally distributed with a mean of minutes and a standard deviation of minutes.

A flight is considered late if it takes longer than minutes.

Calculate the probability a flight is not late.

[4 marks]

A factory that makes bottles knows that, on average, 1.5% of its bottles are defective.

Find the probability that in a randomly selected sample of 20 bottles, at least one bottle is defective.

[4 marks]

The weights, in grams, of oranges grown in an orchard, are normally distributed with a mean of 297 g. It is known that 79 % of the oranges weigh more than 289 g and 9.5 % of the oranges weigh more than 310 g.

(a) Find the probability that an orange weighs between 289 g and 310 g.

(b) The weights of the oranges have a standard deviation of σ. Find the standardized value for 289 g.

[4 marks]

The weight of an adult scallop population are known to be normally distributed with a standard deviation of 5.9 g. If 15% of scallops weight less than 58.2 g, find the mean weight of the population.