Question

Based on a poll, 80% of airline passengers slept or rested during a long flight. Let the random variable x represents the number of airline passengers among the selected six who slept or rested.
A. Construct a table describing the probability distribution and the R Syntax. (2 pts.)
B. Find the probability that at least 2 of the 6 passengers who slept or rested. (2 pts.)
C. Find the mean and standard deviation for the numbers of passengers who slept or rested. (2 pts.)
D. Determine whether 4 is a significantly high number of passengers who slept or rested in a group of 6. Explain. (3 pts.)

Use R:

x P(x)   
0
1
2
3
4
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6

Answer 1

Here, X represents the number of airline passengers among the selected six who slept or rested

p is the probability of airline passengers slept or rested during a long flight

such that n = 6 , p = 0.85 and q = 0.15

Therefore, X ~ Binomial(6,0.85) such that

Answer a.

Part B.

Part C.

Part D.

We can say that 4 is a significantly high number of passengers who slept or rested in a group of 6. Since the probability of 4 people resting is 0.1761 which is 17.61% while the probability of atmost 4 sleeping is 0.2235 collectively which says that there is a lower chance of less than 4 people resting.