a. To List: The mid-point values for the binomial probability.

Isa Trevino

Isa Trevino

Answered question

2021-09-28

a. To List: The mid-point values for the binomial probability.
b. The binomial probability of getting between 57 and 83 successes in a normal distribution probability by using a continuity correction.

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-09-29Added 169 answers

a) Calculation:
The discrete midpoints between the 57 and 83 are 57,58,59,60...81,82,83.
The discrete midpoints at most 54 successes are 0,1,2...53,54.
b) Calculation:
Part (1):
Continuity correction:
The binomial probability is converted to a normal distribution probability by using the continuity correction.
If the binomial probability represents "lies between c1 and c2", then the normal probability is P(c10.5<x<c2+0.5) for any number that is represented by c1 and c2.
Here, the symbol "<" represents "fewer than".
By using continuity correction, the value 0.5 is added to the value of 83 and subtracted from the value of 57.
That is, c1=57 and c2=83.
P(57<x<83)=P(570.5<x<83+0.5)
=P(56.5<x<83.5)
Thus, the binomial probability of getting between 57 and 83 successes in a normal distribution probability by using a continuity correction is P(56.5<x<83.5).
Part (2):
Continuity correction:
If the binomial probability represents "at most c", then the normal probability is P(x<c+0.5) for any number c.
Here, the symbol \leq represents "at most c".
By using continuity correction, the value 0.5 is added to the value of 54.
That is, c=54
P(x54)=P(x<54+0.5)
=P(x<54.5)
Thus, the binomial probability in a normal distribution probability by using continuity correction is P(x<54.5)

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