Question

In a binomial experiment with 45 trials, the probability of more than 25 success can be approximated by What is the probability of success of a single trial of this experiment?

Answer 1

The probability of success for a single trial in this binomial experiment can be found using a formula. We can use the given information to approximate the value of p and find the probability.

Step-by-step explanation:

The probability of success for a single trial in this binomial experiment can be found using the formula o = √(npq), where o is the standard deviation of the experiment, n is the number of trials, p is the probability of success, and q is the probability of failure.

In this case, the number of trials is 45 and the probability of more than 25 successes is given. We can use this information to approximate the value of p by solving the inequality:

P(X > 25) = 1 - P(X <= 25)

P(X > 25) ≈ 1 - binomcdf(45, p, 25) = 0.10

By using this equation, we can solve for p and find the probability of success for a single trial in this experiment.

Answer 2

0.6 is the probability of success of a single trial of the experiment

Complete Problem Statement:

In a binomial experiment with 45 trials, the probability of more than 25 successes can be approximated by
`P(Z>((25-27))/(3.29))`

What is the probability of success of a single trial of this experiment?

Options:

• 0.07
• 0.56
• 0.79
• 0.6

Step-by-step explanation:

So to solve this, we need to use the binomial distribution. When using an approximation of a binomially distributed variable through normal distribution , we get:

`\mu =(np)/(\sigma)`=
`√(np(1-p))`

now,

`Z=(X-\mu)/(\sigma)`

so,

by comparing with
`P(Z>((25-27))/(3.29))`, we get:

μ=np=27

`\sigma=√(np(1-p))` =3.29

put np=27

we get:

`\sigma=√(27(1-p))` =3.29

take square on both sides:

10.8241=27-27p

27p=27-10.8241

p=0.6

Which is the probability of success of a single trial of the experiment