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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In the following problems, use a normal approximation to the binomial.

Management An airport announced a plan to make a special security checkpoint so that first-class passengers would have priority passing through security. Airlines supported this plan, assuming that 25% of passengers would like the idea and it would lead to the sale of more first-class tickets. If this is true, what is the probability that more than 2800 of 10,800 passengers who were surveyed will favor the new policy?

To determine

To calculate: The probability that more than 2800 passengers out of 10800 passengers who were surveyed will favor new policy.

Explanation

Given Information:

An airport announced a plan to make a special security checkpoint for first-class passengers would have priority passing assuming that 25% would like the idea and it will lead to the more sale of the first-class ticket.

Then the probability of more than 2800 successes (inclusive) in n=10800.

Formula used:

For a binomial distribution if, np5 and nq5 then the binomial distribution can be approximated accurately, with mean μ=np and standard deviation σ=npq.

Where n the number of trials, p is the probability of success, and q is the probability of failure q=1p.

And to convert the x values of binomial distribution in use z score use, z=xμσ,

The continuity correction to convert the binomial range of values to the corresponding interval of normal distribution values for any integer x is [x0.5,x+0.5].

Calculation:

Consider that 25% would like the idea and it will lead to the more sale of the first-class ticket.

So, the probability that 25% the passenger will like the idea is p=25%=25100=0.25.

Then the mean is,

μ=npμ=10800(0.25)μ=2700

And the probability of failure is q=1p,

q=10.25q=0.75

And the standard deviation is,

σ=npqσ=10800(0

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