Convert the binomial probability to a normal distribution probability using continuity correction.
P(55< x < 60)

Isa Trevino
2020-12-22
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curwyrm

Answered 2020-12-23
Author has **87** answers

Given binomial probability is P(55 < x < 60), it represents the probability of getting between 55 and 60 successes.
The discrete midpoint values are 55, 56, 57, 58, 59, 60. The corresponding interval for the continuous normal distribution is 54.5 < x < 60.5.
Thus, using the continuity correction, the binomial probability P(55 < x < 60) can be converted into normal distribution probability P(54.5 < x < 60.5).

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Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a dozen frogs.

If the frequency of the trait has not changed, what’s the probability he finds the trait in

a) none of the 12 frogs?

b) at least 2 frogs?

c) 3 or 4 frogs?

d) no more than 4 frogs?

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Getting 2 or 5 in two throws should be $P(2)+P(5)$. $P(2)=1/6,P(5)=1/6$ so the combined so it should be 1/3.

I tried to visualize but not able to do so correctly.

11,12,13,14,15,16, 21,22,23,24,25,26,31,32, ....6,6

total of 36 possibilities.

12,15,21,22,23,24,25,26,31,35,42,45,51,52,53,54,55,56,61,65

out of which 20 possibilities, so the probability should be 20/36 which is not 1/3.

Where am I going wrong?

I tried to visualize but not able to do so correctly.

11,12,13,14,15,16, 21,22,23,24,25,26,31,32, ....6,6

total of 36 possibilities.

12,15,21,22,23,24,25,26,31,35,42,45,51,52,53,54,55,56,61,65

out of which 20 possibilities, so the probability should be 20/36 which is not 1/3.

Where am I going wrong?