An airline does a survey of the weights of adult passengers traveling on its flights. It finds that 5% weigh more than 84.3 kg and 2% weigh less than 57.2 kg. Assuming that the weights of adult passengers on its flight are normally distributed, find the mean of the weights.

A machine poured melted chocolate into moulds. The standard deviation of the amount it pours is 0.7 grams, and the mean amount can be set on the machine. The amount poured may be assumed to follow a normal distribution. The machine is to produce bars whose label says 50 g of chocolate. The company’s lawyers want to have no more than 0.5% of bars containing less than the advertised weight. What should the mean be set at?

There is 1 flaw in a piece of material which is half a meter long.

There is 1 flaw in 3-meter length.

There are no flaws in a 1-meter length.

Allan and Brando start at the same time.

Allan gives Brando a head start of 5 seconds.

Brando gives Allan a head start of 5 seconds.