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# S2 Solomon Questions [Edexcel] watch

1. 1. In an old computer game a white square representing a ball appears at random at the top of the playing area, which is 24 cm wide, and moves down the screen. The continuous random variable X represents the distance, in centimetres, of the dot from the left-hand edge of the screen when it appears. The distribution of X is rectangular over the interval [4, 28].

During a single game, a player receives 12 “balls”.
Q: Find the probability that the ball appears within 3 cm of the middle of the top edge of the playing area more than four times in a single game.

2. Assuming the probability of obtaining more heads than tails is 5/16 when four fair coins are flipped then..

The four coins are flipped 5 times and more heads are obtained than tails 4 times.

Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence of the probability of getting more heads than tails being more than 5/16.

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1. The answer is: let y = no. within 3cm of the middle therefore X~B(12, 0.25)

But how do you get 0.25 as your probability?

2. The answer is 0.0358<0.05 and therefore makes the alt. hypothesis significant but I don't understand how this answer is obtained.

Thanks so much and will plus rep in return.
2. (Original post by Apple24)
1. In an old computer game a white square representing a ball appears at random at the top of the playing area, which is 24 cm wide, and moves down the screen. The continuous random variable X represents the distance, in centimetres, of the dot from the left-hand edge of the screen when it appears. The distribution of X is rectangular over the interval [4, 28].

During a single game, a player receives 12 “balls”.
Q: Find the probability that the ball appears within 3 cm of the middle of the top edge of the playing area more than four times in a single game.

1. The answer is: let y = no. within 3cm of the middle therefore X~B(12, 0.25)

But how do you get 0.25 as your probability?
If X is rectangluar, how is it also binomial? If you mean Y ~ B(12, 0.25) then I'm still confused.

Within 3cm means that you need to cut 6 cms off the 24 cm screen (3 cm from each side), which leaves just 18 cm of the screen. Now since X is rectangular, there's a 1/24 chance of it appear in any one spot. We can allow it to enter any of the 18 spots, so there's an 18/24 = 0.75 chance of it appearing in the desired area. Not sure why they say 0.25.

I'd say Y ~ B(12, 0.75) if Y = the number of balls appearing in the 18 cm area.
3. (Original post by Swayum)
If X is rectangluar, how is it also binomial? If you mean Y ~ B(12, 0.25) then, I'm still confused.

Within 3cm means that you need to cut 6 cms off the 24 cm screen (3 cm from each side), which leaves just 18 cm of the screen. Now since X is rectangular, there's a 1/24 chance of it appear in any one spot. We can allow it to enter any of the 18 spots, so there's an 18/24 = 0.75 chance of it appearing in the desired area. Not sure why they say 0.25.

I'd say Y ~ B(12, 0.75) if Y = the number of balls appearing in the 18 cm area.
Sorry, I did mean Y~B

http://www.mathsandscience.org/resources/S2Fmarks.pdf

Question 3c markscheme
4. Maybe I'm misinterpreting what it means by "within 3 cm" - it could mean that the ball must appear within a 6 cm region in the middle, in which case it'd be 6/24 = 0.25.
5. Thanks very much for your help! I think I understand

Anyone for question two?

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