Question

1. The probability of a man hitting the target at a shooting range is 1/4. If he shoots 30 times, what is the probability that he hits the target at least 10 times?  (Copy your R code and the result).

2. Suppose  X follows a Chi-square distribution with degree of freedom 12. Find the cutoff point a, such that, P(X<a) = 0.85.

3. Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university? (Copy your R code and the result).

4. The following table is the distribution of some game, where W is the money you can win.

W	3	-1	-2
P(W)	0.5	0.2	0.3

        Suppose you play this game 100 times. Find the probability that you will win at least

        $10.

Answer 1

Solution:

The probability of man hitting the target at a shooting range is 1/4.

if the shoots 30 times.

we are calucating the probabality that he hits at least 10 times?

> ## 1

> p=1/4

> n=30

> x=10:30

> ### here we use binomial distribution

> p=sum(dbinom(x,n,p))

> p

[1] 0.1965934

> ## p is the probability of hitting a target at least 10 times

>

> ## 2

> ## x has chi-square distribution

> n=12

> a=qchisq(0.85,n)

> a

[1] 16.98931

> ### a is the required cutoff point i.e.p(x<a)=0.85

>

> ## 3

> ## scores has normal distribution with

> mean=500

> sd=100

> c=qnorm(0.70,mean,sd)

> c

[1] 552.4401

> ## c gives the required mark to be in first 30% of students

> ## tom scores 585 is more than 552

> ##tom wiil be admitted in the university.

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