Answer to Question #123817 in Statistics and Probability for lou

Question

In a certain fitness test for athletes, it is found that 25% of the athletes fail to complete the test. Of the next 15 athletes tested, find the probability that
a) from 3 to 6 fail
b) fewer than 4 fail
c) more than 5 fail
d) determine the mean and standard deviation

Answer 1

Given : n= 15

p=0.25

since the conditions the experiment consists of n identical trials. Each trial results in one of the two outcomes, called success and failure. The probability of success, denoted p, remains the same from trial to trial, we use binomial distribution here.

a)

P($3\leq x\leq 6)$ =P(3)+P(4)+P(5)+P(6)

=0.2252+0.2252+0.1651+0.0917

= 0.7073

b) P(x<4)= P(x=0)+P(x=1)+P(X=2)+P(X=3)

=0.0134+0.0668+0.1559+0.2252

= 0.4613

c)P(X>5)= 1- P(X<=5)

=1- [P(x=0)+P(x=1)+p(X=2)+P(x=3)+P(x=4)+P(x=5)]

= 1-0.0134+0.0668+0.1559+0.2252+0.2252+0.1651

=1- 0.8516

=0.1484

d)mean= np=15*0.25=3.75

sd= $\sqrt{(n*p*(1-p))}$ =$\sqrt{(15*0.25*(1-0.25))}$ =1.677