Question

question 5
approximately 11% of all people are left - handed. consider 25 randomly selected people.
a) state the random variable.
rv x = the number of 25 randomly selected people that are left - handed
b) list the given numeric values with the correct symbols.
n = 25
p = 0.11
c) compute the mean.
round final answer to 2 decimal places.
2.75
which of the following is the correct interpretation of the mean?
out of every 25 people, 2.75 of them on average are left - handed
d) compute the standard deviation.
round final answer to 2 decimal places.
1.56
question help: video 1 video 2

Explanation:

Step1: Identify the distribution

This is a binomial - distribution problem with parameters \(n\) (number of trials) and \(p\) (probability of success). Here, \(n = 25\) (number of people selected) and \(p=0.11\) (probability of a person being left - handed).

Step2: Recall the mean formula for binomial distribution

The mean of a binomial distribution is given by \(\mu=np\). Substitute \(n = 25\) and \(p = 0.11\) into the formula: \(\mu=25\times0.11 = 2.75\).

Step3: Recall the standard - deviation formula for binomial distribution

The standard deviation of a binomial distribution is \(\sigma=\sqrt{np(1 - p)}\). Substitute \(n = 25\) and \(p = 0.11\) into the formula. First, calculate \(1-p=1 - 0.11=0.89\). Then \(np(1 - p)=25\times0.11\times0.89 = 2.4475\). So, \(\sigma=\sqrt{2.4475}\approx1.56\).

Answer:

c) Mean: 2.75
d) Standard deviation: 1.56