Mathematics, 24.02.2020 23:14 joelpimentel

An airline has found about 8% of its passengers request vegetarian meals. On a flight with 162 passengers the airline has 12 vegetarian dinners available. What's the probability that it will be short of vegetarian dinners? (hint: Let X be the number of vegetarians. Identify a probability model for X. Write a probability expression for X that reflects "Short of vegetarian dinners" and compute.)

Answers: 3

Show answers

Answers

Answer from: peralesdavid34

The expression is $P(X \geq 13)$ .

49.60% probability that it will be short of vegetarian dinners.

Step-by-step explanation:

For each passenger, there are only two possible outcomes. Either they request vegetarian meals, or they do not. The probability of a passenger requesting vegetarian meals is independent from other passengers. So we use the binomial probability distribution to solve this problem.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

n = 162, p = 0.08

$\mu = E(X) = np = 162*0.08 = 12.96$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)}[ = \sqrt{162*0.08*0.92} = 3.46$

On a flight with 162 passengers the airline has 12 vegetarian dinners available. What's the probability that it will be short of vegetarian dinners?

If there are 13 or more passengers requesting vegetarian meals, the flight will be short. So the expression is $P(X \geq 13)$ .

This probability is 1 subtracted by the pvalue of Z when X = 13. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{13 - 12.96}{3.46}$

Z = 0.01

Z = 0.01 has a pvalue of 0.5040

1 - 0.5040 = 0.4960

49.60% probability that it will be short of vegetarian dinners.

Answer from: Quest

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24 -24

-3x = -51

2nd step: divide.

-3x = -51

3 3

x = 17

hope this

Answer from: Quest

(0.2)+(-8)=0.3+-3+0.3m is the equation i guess? ?

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:00

The parabola x= √y-9 opens: a.)up b.)down c.)right d.)left

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

What is the explicit rule for the sequence in simplified form? −1,−4,−7,−10,−13… an=4−5n an=−4−3n an=2−3n an=−6−5n

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Find measure angle 1 and measure angle 3 in the kite the diagram is not drawn on the scale

Answers: 1

Answer

Mathematics, 22.06.2019 01:50

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)

Answers: 1

Answer

You know the right answer?

An airline has found about 8% of its passengers request vegetarian meals. On a flight with 162 passe...

Questions