If boys and girls are equally likely to be born what it is t

If boys and girls are equally likely to be born what it is the probability that in a randomly selected family of six children there will be three boys and three girls.(answer .31 need help as to why)

The probability that a person is left-handed is approximately 0.10. What is the expected number of students who are lefthanded in a class of 60 students? (answer 6 need help on how to get that)

The probability that a person is left-handed is approximately 0.10. Let X be the random variable that stands for the number of students who are left-handed in a class of size 60. What is the standard deviation of X?

Find the area under the standard normal curve between z = 0.25 and z = 2.75.

If the area under the standard normal curve that is to the right of z() is , then the number z() is closest to which value below when = 0.9999. (a) 0 (b) more than 3 (c) less than -3 (d)

. What happens to the mean and standard deviation of X as the sample size increases

If a population has a standard deviation = 18.2, what is the standard deviation of the sample mean when a sample of size 49 is selected.

Solution

Q1.
Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

Probability of Boy OR Girl = 0.50

P(will be three boys and three girls) = P( Exactly 3 Boys) = P( X = 3 ) = ( 6 3 ) * ( 0.5^3) * ( 1 - 0.5 )^3
= 0.3125 ~ 0.31