Question

Eighty four percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number of adults who want to live to age 100.
1) Construct a binomial distribution.
2) Graph the binomial distribution using a histogram and describe its shape. Graph the binomial distribution.
3) What is the shape of the histogram?
A. Symmetric
B. Skewed left
C. Skewed right
4) What values of the random variablex would you consider unusual?
The value(s)_____would be unusual because the associated probability (probabilities) is(are)______.

Answer 1

Answer:

1) Binomial distribution with n=5 and p=0.84.

2) Attached. Skewed.

3) C. Skewed right

4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.

Step-by-step explanation:

1) A binomial distribution for this case can be constructed with the parameters n=5 and p=0.84.

The probability of k adults from the sample respond Yes is:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}=\dbinom{5}{k} 0.84^{k}\cdot 0.16^{5-k}$

$P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=1*1*0.0001=0.0001\\\\\\P(x=1) = \dbinom{5}{1} p^{1}(1-p)^{4}=5*0.84*0.0007=0.0028\\\\\\P(x=2) = \dbinom{5}{2} p^{2}(1-p)^{3}=10*0.7056*0.0041=0.0289\\\\\\P(x=3) = \dbinom{5}{3} p^{3}(1-p)^{2}=10*0.5927*0.0256=0.1517\\\\\\P(x=4) = \dbinom{5}{4} p^{4}(1-p)^{1}=5*0.4979*0.16=0.3983\\\\\\P(x=5) = \dbinom{5}{5} p^{5}(1-p)^{0}=1*0.4182*1=0.4182$

2) The graph is attached.

The shape is skewed to the right. This is due to the value of p being close to 1.

The sample space is [0,1,2,3,4,5] and the biggest values have the highest probabilities.

3) The shape is skewed right.

4) The values 0 and 1 would be unusual because the associated probabilities are lower than 0.3%.

The value k=2 can also be considered unusual as it has an associated probability of 2.8%.