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3 years ago

Phone calls arrive at the rate of 48 per hour at the reservation desk for regional airways.

Mathematics

1 answer:

rosijanka [135]3 years ago

4 0

The different probabilities and number of callers expected to be waiting are;

A) P(x = 3) = 0.0286

B) P(x = 13) = 0.1056

C) 8 will be waiting

D) P(x = 0) = 0.0003

E) P(x = 0) = 0.0067

<h3>How to find probability using Poisson distribution?</h3>

We are given the rate of 48 phone calls per hour.

Thus, we will use poisson's distribution formula;

P(x) = (λˣ × e^(-λ))/x!

A) Probability of receiving three calls in a 10-minute interval of time which is P(x = 3). Thus;

λ = 48 * (10/60)

λ = 8

P(x = 3) = (8³ × e⁻⁸)/3!

P(x = 3) = 0.0286

B) Probability of receiving exactly 13 calls in 15 minutes is P(x = 13). Thus;

λ = 48 * (15/60)

λ = 12

P(x = 13) = (12¹³ × e⁻¹²)/13!

P(x = 13) = 0.1056

C) No calls are currently on hold and it takes 10 minutes to complete one call. Thus;

λ = 48 * (10/60)

λ = 8

Thus, 8 will be waiting after 10 minutes.

D) Probability that no one will be waiting is;

P(x = 0) = (8⁰ × e⁻⁸)/0!

P(x = 0) = 0.0003

E) No calls being processed and it takes 5 minutes for a personal time without being interrupted by a call. Thus;

λ = 48 * (5/60)

λ = 4

P(x = 0) = (4⁰ × e⁻⁵)/0!

P(x = 0) = 0.0067

Read more about probability with poisson's distribution at; brainly.com/question/7879375

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The ratio of two numbers is 2/3. The sum of the numbers is 105. What are the two numbers?

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3 years ago

when a ball is dropped onto a flat floor , it bounces to 65% of the height from which it was dropped. if the ball is dropped fro

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3 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

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3 years ago