Find the probability that 200 tosses of a coin will result in (a) between 80 and 120 heads inclusive, (b) less than 90 heads, (c) less than 85 or more than 115 heads, (d) exactly 100 heads.

a)

b)  

c)

d)

Step-by-step explanation:

1) Notation and data given

n= 200 represent the total tosses

p(head)=p(tails)=1/2=0.5 if is a fair coin

The experiment on this case is tossing 200 times a coin

We can calculate np=200*0.5=100>10 and nq=n(1-p)=200*(1-0.5)=100>10

So then since np>10 and nq>10 we can use the approximation normal to the binomial distribution.

Let X our random variable who represents "the number of heads obtained in 200 tosses from a fair coin". This random variable X follows a normal distribution. And since we have all the conditions satisfied we can calculate the mean and the deviation for the normal distribution

Since X follows a normal distribution we can standarize on this way

And z is distributed normal with mean= and deviation =1.

This z score would be useful in order to calculate the probabilities required.

2) Part a

Using properties from the normal distribution we have this

3) Part b

And using a the normal standard distribution table or excel we find that:

4) Part c

Since the events and are independent, so we can find the probability like this

So we can find individually the probabilities like this:

So then:

5) Part d

If we use the normal approximation since the area below the curve for a point is not defined. Then the probability P(X=100) would be 0.

answer: 140

step-by-step explanation:

so just add all then it will be your answer but i am not pretty sur eif it is but hope this i am here to people

the answer would be d

straight away you can eliminate a and c because not all books contain a scientific skill because some may be fiction. c is also wrong because it saids that the only way children can learn is through books which is incorrect.

b is also wrong because reading can be a scientific skill but not always, therefore it is wrong which leaves you with d, the correct answer since it said that it can children learn.

hope this ! : 3