Math Is Fun Forum

An airline knows that some people who have bought tickets may not arrive for the flight. The airline therefore sells more tickets than the number of seats that are available. For one flight there are 210 seats available and 213 people have bought tickets. The probability of any person who has bought a ticket not arriving for the flight is 1 .
50
(i) Byconsideringthenumberofpeoplewhodonotarrivefortheflight,useasuitableapproximation to calculate the probability that more people will arrive than there are seats available. [4]
Independently, on another flight for which 135 people have bought tickets, the probability of any
person not arriving is 1 . 75
(ii) Calculate the probability that, for both these flights, the total number of people who do not arrive is 5. [3]

Can anyone explain to me how to do part (i)

Roger thinks that a box contains 6 screws and 94 nails. Felix thinks that the box contains 30 screws and 70 nails. In order to test these assumptions they decide to take 5 items at random from the box and inspect them, replacing each item after it has been inspected, and accept Roger’s hypothesis (the null hypothesis) if all 5 items are nails.
(a) Calculate the probability of a Type I error. [4]
(b) If Felix’s hypothesis (the alternative hypothesis) is true, calculate the probability of a Type II
error.
[3]

2 In summer the growth rate of grass in a lawn has a normal distribution with mean 3.2 cm per week and standard deviation 1.4 cm per week. A new type of grass is introduced which the manufacturer claims has a slower growth rate. A hypothesis test of this claim at the 5% significance level was carried out using a random sample of 10 lawns that had the new grass. It may be assumed that the growth
rate of the new grass has a normal distribution with standard deviation 1.4 cm per week.
(i) Find the rejection region for the test. [4]
(ii) The probability of making a Type II error when the actual value of the mean growth rate of the new grass is m cm per week is less than 0.5. Use your answer to part (i) to write down an inequality for m. [1]

part (ii) ans : m<2.47: roflol