The value given below is discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. Probability of exactly 4passengers who do not show up for a flightChoose the correct answer below. A.The area between 3.5 and 4.5 B.The area to the left of 4.5 C.The area to the right of 3.5 D.The area to the left of 3.5 E.The area to the right of 4.5

Question
Asked Apr 27, 2019
The value given below is discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. Probability of exactly 4passengers who do not show up for a flight
Choose the correct answer below.
 
A.The area between 3.5 and 4.5
 
B.The area to the left of 4.5
 
C.The area to the right of 3.5
 
D.The area to the left of 3.5
 
E.The area to the right of 4.5
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Expert Answer

Step 1

Continuity correction:

Continuity correction is used to approximate a discrete distribution to a continuous distribution. In general, normal distribution is used in approximating the discrete distribution to continuous distribution.

The probability of a discrete random variable is converted to normal distribution probability by using the continuity correction as follows:

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Step 2

Convert the discrete probability to continuous probability:

A random variable x denotes the number of passengers who do not show up for a flight.

The variable x takes countable or finite values. Therefore, x is a discrete variable.

Here, the number of passengers who do not show up for a flight is equal to 4. That is, x = 4.

If the discrete probability represents “exactly c” then the normal probability is P(c – 0.5 < x < c + 0.5) for any number c.

The discrete probability x = 4 is converted to normal probability as given below:

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Step 3

Choose the correct answer:

The discrete probability x = 4 is converted to normal probability as P( 3.5 < x < 4.5).

Therefore, the region of the normal distribution that...

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