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Maths statistics question

Every weekday Mr Bullar, a teacher, leaves home early in the hope that his favourite car parking spot is available at school. On average he finds that he gets this spot on one day out of three. Let the random variable X represent the number of days in a working week of 5 days that Mr Bullar parks in his favourite spot.
(a) In order to use a binomial distribution model for X, state one assumption you will need to make.
(b) Calculate the probability that Mr Bullar parks in his favourite spot on at least 2 weekdays in a given week.

There are seven school weeks in the next half term. Mr Bullar thinks it’s a good week if
he parks in his favourite spot on more than one day in the week, otherwise he calls it a bad week.

(c) Calculate the probability that Mr Bullar has more good weeks than bad weeks next Half term.

So
A) we assume that probability of the spot being empty is the same for each day.
B) X-P(5,2/5)
1-P(X=1)-(X=0)
1-0.2592-0.0777=0.66 sf

C) do I draw a tree diagram for C?
Also, for B is my model correct since in the question it says 2 days in a week day.
So I think n would be 7 but Not sure so I put 5.
Can someone help me out😂

I know the question

Original post by Tregi11

C) do I draw a tree diagram for C?
Also, for B is my model correct since in the question it says 2 days in a week day.
So I think n would be 7 but Not sure so I put 5.
Can someone help me out😂

(C) is another binomial problem: (B) gives you the probability of a "good" week, and you're now dealing with how many "good" weeks you have in 7 trials (weeks).
[The examiners seem to really like these 2 part questions where the probability you find in the first part becomes the "p" value for a binomial in the 2nd part. Seems a bit stupid/repetitive to me, but what can you do].

a "week day" is one of Mon, Tues, Weds, Thurs, Fri (i.e. not a weekend). https://www.thefreedictionary.com/weekday

So n = 5 is correct.

Reply 3

username5568728

For part B, look again at the value for p you used. The probability is not the number of times he gets the parking space in a week. It is 'at least' so should you use cumulative probability?

For part C, work out the probability that he gets the spot more than once (did you work it out in question B). That is your p, n is the number of weeks. You work out the probability for more good weeks than bad weeks - so 4 or 3?

Reply 4

DFranklin

Original post by Lily_23

For part B, look again at the value for p you used. The probability is not the number of times he gets the parking space in a week. It is 'at least' so should you use cumulative probability?

Seems OK to me; the OP has calculated 1 - p(0 times) - p(1 time) which equals p(>=2 times).

Reply 5

ghostwalker

Original post by DFranklin

Seems OK to me; the OP has calculated 1 - p(0 times) - p(1 time) which equals p(>=2 times).

Formula is fine, but the calculation itself has issues. P(X=0)= 0.0777 implies they used p=0.4 (the 2/5 in their binomial defintion).

I had almost completed an original reply to the first post when TSR/my machine threw a wobbly and lost it all, apart from one word - "false" - and I didn't even type that one in.

(edited 3 years ago)

Reply 6

Tregi11

Original post by ghostwalker

So, if P is not 2/5 what is it?How am I meant to find the P

Reply 7

ghostwalker

Original post by Tregi11

So, if P is not 2/5 what is it?How am I meant to find the P

Reread the original question - in particular, what information haven't you used.

I'll post again if you can't see it, but do have a look first.

Reply 8

Tregi11

Original post by ghostwalker

Reread the original question - in particular, what information haven't you used.

I'll post again if you can't see it, but do have a look first.

Oh yeah I got it sorry for the trouble😂thanks

Reply 9

ghostwalker

Original post by Tregi11

Oh yeah I got it sorry for the trouble😂thanks

No problem. It's always more useful to you if you can resolve the issue yourself.

help plz

Original post by Tregi11

Every weekday Mr Bullar, a teacher, leaves home early in the hope that his favourite car parking spot is available at school. On average he finds that he gets this spot on one day out of three. Let the random variable X represent the number of days in a working week of 5 days that Mr Bullar parks in his favourite spot.
(a) In order to use a binomial distribution model for X, state one assumption you will need to make.
(b) Calculate the probability that Mr Bullar parks in his favourite spot on at least 2 weekdays in a given week.
There are seven school weeks in the next half term. Mr Bullar thinks it’s a good week if
he parks in his favourite spot on more than one day in the week, otherwise he calls it a bad week.
(c) Calculate the probability that Mr Bullar has more good weeks than bad weeks next Half term.
So
A) we assume that probability of the spot being empty is the same for each day.
B) X-P(5,2/5)
1-P(X=1)-(X=0)
1-0.2592-0.0777=0.66 sf
C) do I draw a tree diagram for C?
Also, for B is my model correct since in the question it says 2 days in a week day.
So I think n would be 7 but Not sure so I put 5.
Can someone help me out😂

Abit late but for anyone else wondering how to do this questions, I will explain.

a) Binomial distribution only works if events are independent of each day e.g if he parks there 1 day, he has the same probability of parking there the next day.
b) Will need to use the binomial distribution formula x-b(n,p)
n will be the number of attempts (number of days), and p is the probability of success which is mentioned in the question
Then work out the P(x>=2)=1-P(x<=1) (Use Binomial CD on your calculator)
c) Use your answer form b as your probability (p) and use the number of weeks as the n so you will need to write another binomial expression e.g. Y-B(n,p)
The probability of having more good weeks than bads will be weeks>=4
so find P(Y>=4) the same way as b