Question

At 8:14 am on a typical day, 75.0% of the cars entering York University fron Keele St come from the north and 25.0% come from the south. On a particular day, 729 cars entered from the north and 301 cars from the south. (a) (2 marks) What are the theoretical uncertainties in the latter two numbers? (b) (8 marks) What is the probability that these counts were not made on a "typical day"? In other words, find the probability of obtaining a result that is as far or urther from the mean than the results measured on the particular dav

Answer 1

a)

HERE on a typicall day 75% chances are their for north and 25% for south

so out of 1030 total cars 729 from north and 301 from south.

but theoretically they should be 75% and 25% of 1030 i.e 772 and 258

so clearly these number are very uncertain theoritically.

b)

let X be the number of cars from north out of 1030

then X~binomial(n,p) n 1030 p as 0.75

P(|X-mean|>= |729-mean|)

i.e putting mean as n*p i.e 772.5 also 772.5-729 is43.5

P(X>=816 or x<=729)

(pbinom(729,1030,.75)) + 1-(pbinom(815,1030,.75))
0.00196941

required probavility is 0.00196941