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Bookmarks People Window Halp ileyplus.com/edugen/student/mainfr.uni BUSINESS STATISTICS (ECON 245) Black, Business Statistics, 8e 09:42 PM/Remaining 10 min, Question 10 A Department of Transportation survey showed that 60% of U.S. residents over 65 years of age oppose use of cet phones in fight even if there were no issues with the phones interfering with aircraft communications systems. If this information is correct and if a researcher randomly selects 25 U.S. residents who are over 65 years of age, a. What is the probability that exactly 12 oppose the use of cell phones in fight? b. What is the probabilty that more than 17 oppose the use of cell phones in fight? c. What is the probability that less than eight oppose the use of cell phones in fiight? If the researcher actually got less than eight, what might she conclude about the Department of Transportation survey? *(Round your answers to 3 decimal places when calculating using IableA2.) (Round your answer to 1 decimal places.) (Round your answer to 0 decimal places.) a. P(x 12, l n 25 and p .60 b. P(x 17 l n 25 and p -60) PCX 8 I n 25 and p .60) L of the time by chance, it is likely that the researcher's sample was Since such a result would only occur not representative of the U.S, residents over 65 years of age or the figure is not correct for the Question Attempts: 0 of 1 used SAVE FOR LATER SUBMIT ANSWER Policy 1 2000 2016 lobo Wae.A Saas Inc. All Rights Reserved A Division of 2pha Sona une version 4.17.3. reduassignmenthest/agist unie MacBook Air

Explanation / Answer

Let X be the random variable that number of 65 years of age oppose use of cell phones in flight.

X ~ Binomial(n=25, p= 0.60)

All the probabilities we can find by using EXCEL.

syntax is,

=BINOMDIST(number_s, trials, probability_s, cumulative)

where

Number_s   is the number of successes in trials.

Trials   is the number of independent trials.

Probability_s   is the probability of success on each trial.

Cumulative   is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

First we have to find P(X=12).

EXCEL syntax is,

=BINOMDIST(number_s, trials, probability_s, cumulative)

number_s = 12

trials = 25

probability_s = 0.60

cumulative = False

P(X=12) = 0.076

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P(X>17) = P(X=18 or 19 or 20 or 21 or 22 or 23 or 24 or 25)

= P(X=18) + P(X=19) + P(X=20) + P(X=21) + P(X=22) + P(X=23) + P(X=24) + P(X=25)

By using EXCEL the table of x and probabilities is,

x   p
18   0.080
19   0.044
20   0.020
21   0.007
22   0.002
23   0.000
24   0.000
25   0.000
total   0.154

P(X > 17) = 0.154

----------------------------------------------------------------------------------------------------------------------------------------------------------

P(X < 8) = P(X=0 or 1 or 2 or 3 or 4 or 5 or 6 or 7)

= P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)

x_1   p_1
0   0.0000000
1   0.0000000
2   0.0000001
3   0.0000009
4   0.0000072
5   0.0000454
6   0.0002271
7   0.0009247
   0.0010000

P(X < 8) = 0.001

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