A binomial probability is given. Write the probability in words. Then, use a con

CoormaBak9

CoormaBak9

Answered question

2021-09-25

A binomial probability is given. Write the probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability:
P(x>116)
Write the probability in words.
The probability of getting _ 116 successes.
Which of the following is the normal probability statement that corresponds to the binomial probability statement?
A. P(x>116.5)
B. P(x>115.5)
C. P(115.5<x<116.5)
D. P(x<115.5)
E. P(x<116.5)

Answer & Explanation

estenutC

estenutC

Skilled2021-09-26Added 81 answers

Step 1
Solution:
Given information:
The binomial probability is
P(x116)
Step 2
The binomial probability in words is
The probability of getting at most 116 successes .
The continuity correction factor can be used to convert discrete probability into the continuous probability.
By Central limit theorem the sampling distribution of sample mean approaches to the normal distribution if the sample
size n gets larger (n>30).
In binomial distribution if both np and nq both greater than or equal to 10 or 5 then the binomial distribution can be approximated to the normal distribution.
When we used continuity correction factor to convert discrete probability into continuous probability it is just adding or subtracting 0.5 to the discrete x value
The given binomial probability can be converted to normal probability is
P(x116) use P(x<116+0.5)
P(x116)=P(x<116.5)
The normal probability statement P(x<116.5) is correspond to the binomial probability statement P(x116)
Option E is correct.

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