Question

A study indicates that 37% of students have laptops. You randomly sample 30 students. Find the mean and the standard deviation of the number of students with laptops.

Answer 1

Answer:

The mean and the standard deviation of the number of students with laptops are 1.11 and 0.836 respectively.

Step-by-step explanation:

Let X = number of students who have laptops.

The probability of a student having a laptop is, P (X) = p = 0.37.

A random sample of n = 30 students is selected.

The event of a student having a laptop is independent of the other students.

The random variable X follows a Binomial distribution with parameters n and p.

The mean and standard deviation of a binomial random variable X are:

$\mu=np\\\sigma=\sqrt{np(1-p)}$

Compute the mean of the random variable X as follows:

$\mu=np=30\times0.37=1.11$

The mean of the random variable X is 1.11.

Compute the standard deviation of the random variable X as follows:

$\sigma=\sqrt{np(1-p)}=\sqrt{30\times0.37\times(1-0.37)}=\sqrt{0.6993}=0.836$

The standard deviation of the random variable X is 0.836.