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

answered: 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.

answered: Guest

hi, i am not sure about this one but i think its d,

hope this !

Which figure. does not appear to be congruent to the figure below

answered: Guest

Igxtfuvu cube b kisooaokajsvd wkisvhikbg $26$

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:30, auzriannamarie

Tim's phone service charges $26.39 plus an additional $0.21 for each text message sent per month. if tim's phone bill was $31.64, which equation could be used to find how many text messages, x, tim sent last month?

Answers: 1

continue

Mathematics, 21.06.2019 22:30, jakails359

Atotal of 766 tickets were sold for the school play. they were either adult tickets or student tickets. there were 66 more student tickets sold than adult tickets. how many adult tickets were sold?

Answers: 1

continue

Mathematics, 21.06.2019 23:00, leverso

You buy a veido game for $60 and the sales tax is 8% what is the total cost for the game including the sales tax

Answers: 1

continue

Mathematics, 22.06.2019 00:00, Lions8457

City l has a temperature of −3 °f. city m has a temperature of −7 °f. use the number line shown to answer the questions: number line from negative 8 to positive 8 in increments of 1 is shown. part a: write an inequality to compare the temperatures of the two cities. (3 points) part b: explain what the inequality means in relation to the positions of these numbers on the number line. (4 points) part c: use the number line to explain which city is warmer. (3 points)

Answers: 2

continue

Do you know the correct answer?

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