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2 years ago

10

a student has a 73% of being let out of class late. if he leaves class late. if he leaves class late, there is a 23% chance that

he will miss his train. what is the probability that he gets out of class late and misses the train?

2 answers:

Elza [17]2 years ago

8 0

Answer:

16.79 %

Step-by-step explanation:

hythjuuhhhjuhhhh

4vir4ik [10]2 years ago

4 0

The answers is 16.79

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2 years ago

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851-473 is the same as ___[dash]-470

Degger [83]

First figure out what 851 minutes 473 equals to, which is 378

So both sides of the equation should equal to 378

Plus 470 and 378 together

Which equals to 848

So the answer is eight hundred and forty eight

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3 years ago

Short sleeve t-shirts cost $10 and long sleeve t-shirts cost $15. If the t-shirt shop made $485 selling 38 total t-shirts, how m

BartSMP [9]

Answer:

The t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.

Step-by-step explanation:

To solve this problem, we should create a system of equations. Let's let short sleeve t-shirts be represented by the variable s and long sleeve t-shirts be represented by the variable l.

We know that the shop sold 38 total shirts, or in other words, the amount of long sleeve and short sleeve shirts combined is 38. If we write this as an equation, we get: s + l = 38.

We can make another equation with the prices of the shirts. If we take each type of shirt and multiply each price by the number sold and add them together, we should get the shop's total profits. Represented as an equation, this is: 10s + 15l = 485.

Now that we have two equations, we should try to solve the system. In this case, it is easiest to use substitution, so we are going to rewrite the first equation in terms of one variable.

s + l = 38

s = 38 - l

If we substitute this equivalent value for the variable s into the second equation, we get:

10s + 15l = 485

10(38 - l) + 15l = 485

Now we have an equation that only has one variable, so we can simplify both sides and then isolate the variable.

380 - 10l + 15l = 485

380 + 5l = 485

5l = 105

l = 21

Now, we can substitute this value for l back into the first equation to solve for the variable s.

s + l = 38

s + 21 = 38

s = 17

Therefore, the t-shirt shop sold 21 long sleeve shirts and 17 short sleeve shirts.

Hope this helps!

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3 years ago

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3 years ago

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 12

melamori03 [73]

Answer:

98.75% probability that every passenger who shows up can take the flight

Step-by-step explanation:

For each passenger who show up, there are only two possible outcomes. Either they can take the flight, or they do not. The probability of a passenger taking the flight is independent from other passenger. So the binomial probability distribution is used to solve this question.

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

The probability that a passenger does not show up is 0.10:

This means that the probability of showing up is 1-0.1 = 0.9. So $p = 0.9$

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets

This means that $n = 125$

Using the approximation:

$\mu = E(X) = np = 125*0.9 = 112.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.9*0.1} = 3.354$

(a) What is the probability that every passenger who shows up can take the flight

This is $P(X \leq 120)$ , so this is the pvalue of Z when X = 120.

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

$Z = \frac{120 - 112.5}{3.354}$

$Z = 2.24$

$Z = 2.24$ has a pvalue of 0.9875

98.75% probability that every passenger who shows up can take the flight

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3 years ago