24 internet use a survey of us adults ages 50 64 found that...

'24 Internet Use A survey of U.S adults ages 50-64 found that 70% use the Internet: You randomly select 80 adults ages 50-64 and ask them if they use the Internet: (Source: Pew Research Center) (a) Find the probability that at least 70 people say they use the Internet: (b) Find the probability that exactly 50 people say they use the Internet: (c) Find the probability that more than 60 people say they use the Internet. (d) Are any of the probabilities in parts (a)-(c) unusual? Explain:'

Transcript

00:01 In this question we're given from a survey, 70 % of us adults aged 50 to 64 use the internet.

00:08 80 adults in this age group are randomly selected.

00:12 I'm going to let x be the number of adults out of the 80 in this sample who use the internet.

00:17 Now n, the number of trials, would be 80 since there are 80 adults.

00:21 In each trial we take a look at the adult in this sample and see whether he or she use the internet or not.

00:25 So all these 80 trials are identical and independent and we have p probability of success in a single trial, that's probability an adult in this age group use the internet and that'll be 70 % or 0 .7 decimal.

00:41 And this remains constant for all the trials.

00:44 So x follows the binomial distribution, n is 80, p is 0 .7.

00:53 But n is 80 is greater than 50, n times p, 80 times 0 .7, we'll get 56 which is greater than 5.

01:05 And we have n times 1 minus p and that will be 24 which is greater than 5.

01:14 Now these three criterias here shows that we, x actually can follow the normal distribution approximately with the mean as np which is 56 and the variance will be np times 1 minus p and that would be 16 .8.

01:39 Now because x was originally binomial which is discrete and now it follows normal distribution which is continuous, we have to use continuity correction.

01:50 In part a, we want to find probability at least 70 people say they use the internet.

01:55 So we're looking at probability of x greater equals to 70.

02:00 So by using continuity correction, i'll call it cc, we will be using this one here that is probability x greater than 70 minus 0 .5.

02:15 And so we're looking at probability of x greater than 69 .5.

02:19 Let's draw the distribution for x.

02:24 The mean is 56, 69 .5 is over here and x greater than that is this shaded area we're talking about.

02:32 I'll be using the ti -84 calculator, the normal cdf function.

02:40 Now to key in a lower limit and there'll be 69 .5.

02:45 Key in upper limit and there'll be a large positive number.

02:50 So usually i'll key in 10 to the power 99.

02:53 Mu is the mean of x and that's 56.

02:56 Sigma is the standard deviation of x and that will be the square root of the variance which is 16 .8.