question 5\napproximately 11% of all people are left - handed. consider 25 randomly selected people.\na)…

question 5\napproximately 11% of all people are left - handed. consider 25 randomly selected people.\na) state the random variable.\nrv x = the number of 25 randomly selected people that are left - handed\nb) list the given numeric values with the correct symbols.\nn = 25\np = 0.11\nc) compute the mean.\nround final answer to 2 decimal places.\n2.75\nwhich of the following is the correct interpretation of the mean?\nout of every 25 people, 2.75 of them on average are left - handed\nd) compute the standard deviation.\nround final answer to 2 decimal places.\n1.56\nquestion help: video 1 video 2

question 5\napproximately 11% of all people are left - handed. consider 25 randomly selected people.\na) state the random variable.\nrv x = the number of 25 randomly selected people that are left - handed\nb) list the given numeric values with the correct symbols.\nn = 25\np = 0.11\nc) compute the mean.\nround final answer to 2 decimal places.\n2.75\nwhich of the following is the correct interpretation of the mean?\nout of every 25 people, 2.75 of them on average are left - handed\nd) compute the standard deviation.\nround final answer to 2 decimal places.\n1.56\nquestion help: video 1 video 2

Answer

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