Mathematics, 20.02.2020 08:08 mari33312

A man claims to have extrasensory perception. As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 25 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP?

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Answer from: JamlessJimin

$P(25 \leq x \leq 28)=P(X=25)+P(X=26)+P(X=27)+P(X=28)$

Using the probability mass function we got:

$P(X=25)=(28C25)(0.5)^{25} (1-0.5)^{28-25}=0.0000122$

$P(X=26)=(28C26)(0.5)^{26} (1-0.5)^{28-26}=0.00000141$

$P(X=27)=(28C27)(0.5)^{27} (1-0.5)^{28-27}=0.000000104$

$P(X=28)=(28C28)(0.5)^{28} (1-0.5)^{28-28}=3.75x10^{-9}$

And adding the probabilities we got:

$P(25 \leq X \leq 28) = 0.00001372$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n, p)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

For a fair coin flip n=28 times we have the following distribution:

$X \sim Binom(n=28, p=0.5)$

We want to find this probability:

$P(25 \leq x \leq 28)=P(X=25)+P(X=26)+P(X=27)+P(X=28)$

Using the probability mass function we got:

$P(X=25)=(28C25)(0.5)^{25} (1-0.5)^{28-25}=0.0000122$

$P(X=26)=(28C26)(0.5)^{26} (1-0.5)^{28-26}=0.00000141$

$P(X=27)=(28C27)(0.5)^{27} (1-0.5)^{28-27}=0.000000104$

$P(X=28)=(28C28)(0.5)^{28} (1-0.5)^{28-28}=3.75x10^{-9}$

And adding the probabilities we got:

$P(25 \leq X \leq 28) = 0.00001372$

Answer from: Quest

b. the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

Answer from: Quest

81 seats

step-by-step explanation:

if you multiply 0.65 times 125 then you get 81.5 seats. well since you can't have half of a seat you have to round down and get 81 seats in the no children zones. that leave 44 seats outside of the no children zone.