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Lostsunrise [7]
3 years ago
14

An airline reports that it has been experiencing a 15% rate of no-shows on advanced reservations. Among 150 advanced reservation

s, find the probability that there will be less than 20 no-shows. Use the normal distribution to approximate the binomial distribution.
Mathematics
1 answer:
forsale [732]3 years ago
3 0

Answer:

[tex]P(X

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=150, p=0.15)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

We need to check the conditions in order to use the normal approximation.

np=150*0.15=22.5 \geq 10

n(1-p)=150*(1-0.15)=127.5 \geq 10

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

E(X)=np=150*0.15=22.5

\sigma=\sqrt{np(1-p)}=\sqrt{150*0.15(1-0.15)}=4.373

So then our random variable can be distributed on this way:

X \sim N(\mu =22.5, \sigma=4.373)

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability on this way:

P(Z

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Answer:

b. (3,0)

e. (5,-6)

f. (2,1)

Are solutions to the system of inequalities

Step-by-step explanation:

b. (3,0)

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0 ≤ 0 is true

3 > 1 is true

e. (5,-6)

-6 ≤ -2(5)+6

-6 ≤ -4 is true

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f. (2,1)

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Use a calculator to solve this problem:<br><br> 28 + 27 × 36
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28 + 27 * 36 =\\28 + 972 =\\1000

Thus, the value of the expression is 1000.

Answer:

28 + 27 * 36 = 1000

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The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than
svlad2 [7]

The shop sold 36 sundaes and 28 banana spilts

<em><u>Solution:</u></em>

Let "a" be the number of sundaes sold

Let "b" be the number of banana spilts sold

Cost of 1 sundaes = $ 2

Cost of 1 banana spilt = $ 3

<em><u>On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156</u></em>

Therefore,

Number of sundaes sold = 8 + number of banana spilts sold

a = 8 + b ------- eqn 1

<em><u>Also, given that they made $ 156</u></em>

<em><u>Therefore, we frame a equation as</u></em>:

Number of sundaes sold x Cost of 1 sundaes + number of banana spilts sold x Cost of 1 banana spilt = 156

a \times 2+b \times 3 = 156

2a + 3b = 156 ---------- eqn 2

<em><u>Substitute eqn 1 into eqn 2</u></em>

2(8 + b) + 3b = 156

16 + 2b + 3b = 156

16 + 5b = 156

5b = 156 - 16

5b = 140

<h3>b = 28</h3>

<em><u>Substitute b = 28 in eqn 1</u></em>

a = 8 + 28

<h3>a = 36</h3>

Thus the shop sold 36 sundaes and 28 banana spilts

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It takes 2 hours to drive 80 miles and 4 hours to drive 160 miles. Find the rate of change. I need this asap
natita [175]

Answer:

40 miles per hour

Step-by-step explanation:

80 divided by  2 is 40

160 divided by 4 is 40

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