Can you confirm if my methods of working out and the answers are correct for the following question?
the question
Malaysia (MAL) is a highly tactical team and puts a lot of emphasis on how far their players can 'Header' a ball. The distance that the MAL players can Header the ball is normally distributed with a mean of 18 metres and standard deviation of 3 metres.
a. Find the probability, correct to 3 decimal places, that a MAL player can Header at least 20 metres (2 marks)
my working and my answer
I did X ~ N (18,32)
Using the normCdf function, I got 0.252.
b. 8 of the MAL players are selected at random and asked to header the ball at training. Find the probability correct to 3 decimal places that:
i. Only the first two players Header the ball at least 20 metres. (2 marks)
my working and my answer
X ~ Bi(8, 0.252).
Using the binomCdf function, I got 0.638
ii. Exactly 2 of the players Header the ball at least 20 metres. (2 marks)
my working and my answer
X ~ Bi(8, 0.252)
Using the binomPdf function, I got 0.311
iii. At least 4 of the players Header the ball at least 20 metres, given the first player chosen Headers the ball at least 20 metres (2 marks)
my working and my answer
Using the conditional probability formula, I got 0.117.
The below section is the source of my uncertainty and confusion. (It doesn't help that it's badly worded)
c. Find the minimum number of MAL players required to ensure that the probability that at least one of them can Header the ball at least 20 metres is at least 0.98. (3 marks)
I started by doing Pr(X≥1) = 0.98 but then my calculator exposed my ignorance. Makes no sense, doesn't it? Now I don't know what to do for this particular question.
Hopefully I typed up enough information to enable you to help me out! Thanks!