Mathematics, 02.03.2020 19:19 imaboss10986

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. Suppose that a random sample of n = 49 customers is observed. Find the probability that the average waiting time in line for these customers is

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Answer from: dwarfarmy99

Part a

$P(\bar X$

And using a calculator, excel or the normal standard table we have that:

P(Z

Part b

P(5

And using a calculator, excel or the normal standard table we have that:

P(-14.933

Part c

$P(\bar X$

And using a calculator, excel or the normal standard table we have that:

P(Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the time waiting at an airport check in of a population, and for this case we know the distribution for X is given by:

$X \sim N(8.2,1.5)$

Where $\mu=8.2$ and $\sigma=1.5$

We select a random sample of n = 49. Since the distribution of X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can find the individual probabilities like this:

Part a

$P(\bar X$

And using a calculator, excel or the normal standard table we have that:

P(Z

Part b

P(5

And using a calculator, excel or the normal standard table we have that:

P(-14.933

Part c

$P(\bar X$

And using a calculator, excel or the normal standard table we have that:

P(Z

Answer from: Quest

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Answer from: Quest

may i see the picture? it would a lot, xox

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The amount of time that a customer spends waiting at an airport check-in counter is a random variabl...