Seventy-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 variablerepresents the number of adults who want to live to age 100. Complete parts (a) through (c) below.(a) Construct a binomial distribution.P(x)0.13.4(Round to five decimal places as needed.)(b) Graph the binomial distribution using a histogram and describe its shape.Graph the binomial distribution. Choose the correct graph below.O A.O B.Oc.O D.Living to Age100Living to Age100Living to Age100Living to Age1000.5-0.5-0.5-0.5-(1,1)MoreClick to select your answer(s).HUAWEIProbabilityProbabilityProbabilityProbability

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Seventy-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. Complete parts (a) through (c) below.
(a) Construct a binomial distribution.
P(x)
0.
1
3.
4
(Round to five decimal places as needed.)
(b) Graph the binomial distribution using a histogram and describe its shape.
Graph the binomial distribution. Choose the correct graph below.
O A.
O B.
Oc.
O D.
Living to Age
100
Living to Age
100
Living to Age
100
Living to Age
100
0.5-
0.5-
0.5-
0.5-
(1,1)
More
Click to select your answer(s).
HUAWEI
Probability
Probability
Probability
Probability

Expert Solution

Step 1

Given Information:

74% of adults want to live to age 100. i.e., $p = 0.74$

Sample size (n) = 5

(a) Construct a Binomial distribution:

Binomial formula:

$P (X = x) = {}^{n}C_{x} p^{x} {(1 - p)}^{n - x}$

For X = 0, P(0) is obtained as follows:

$\begin{array}{rcl} P (X = 0) & = & {}^{5}C_{0} {(0.74)}^{0} {(1 - 0.74)}^{5 - 0} \\ = & 1 \times 1 \times 0.00119 \\ = & 0.00119 \end{array}$

For X = 1, P(1) is calculated as follows:

$\begin{array}{rcl} P (X = 1) & = & {}^{5}C_{1} {(0.74)}^{1} {(1 - 0.74)}^{5 - 1} \\ = & 5 \times 0.74 \times 0.00456976 \\ = & 0.016908112 \\ \approx & 0.01691 \end{array}$

For X = 2, P(2) is obtained as follows:

$\begin{array}{rcl} P (X = 0) & = & {}^{5}C_{2} {(0.74)}^{2} {(1 - 0.74)}^{5 - 2} \\ = & 10 \times 0.5476 \times 0.017576 \\ \approx & 0.09625 \end{array}$

For X = 3, P(3) is obtained as follows:

$\begin{array}{rcl} P (X = 3) & = & {}^{5}C_{3} {(0.74)}^{3} {(1 - 0.74)}^{5 - 3} \\ = & 10 \times 0.405224 \times 0.0676 \\ \approx & 0.27393 \end{array}$

For X = 4, P(4) is obtained as follows:

$\begin{array}{rcl} P (X = 4) & = & {}^{5}C_{4} {(0.74)}^{4} {(1 - 0.74)}^{5 - 4} \\ = & 5 \times 0.29986576 \times 0.26 \\ \approx & 0.38983 \end{array}$

For X =5, P(5) is obtained as follows:

$\begin{array}{rcl} P (X = 5) & = & {}^{5}C_{5} {(0.74)}^{5} {(1 - 0.74)}^{5 - 5} \\ = & 1 \times 0.2219006624 \times 1 \\ \approx & 0.22190 \end{array}$

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