Match each histogram to the binomial parameters n and p that correctly character

Question

Match each histogram to the binomial parameters n and p that correctly characterize it, where p indicates the probability of success for each of the n trials.

Please match each histogram to one of the categories below the charts (i.e. "n = 40, p = 0.2" is matched with whatever histogram above). Categories can be used more than once.

Match each histogram to the binomial parameters n and p that correctly characterize it, where p indicates the probability of success for each of the n trials Histogram A Histogram B Histogram C 0.15 0.12 0.07 0.10 0.08 -? 0.050- 0.05 0.04 0.025 0.00 0.00 0. 0 5 1015 20 25 10 20 30 40 Number of Successes Histogram E 0 40 50 60 7080 90 Number of successes Number of successes Histogram D 0.15 0.20 0.10 0.15 0.10 0.05 0.05 0.00 0.00 20 30 15 20 Number of successes 0 10 Number of successes n = 40, p = 0.2 n-30, p-0.4 n 40,p0.5 n-100, p 0.7 n-30, p-0.9

Explanation / Answer

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We use the help of binomial distribution mean formula to get this answer. We know that for any binomila distribution with params, n and p, Mean = n*p. So, lets use this to get our answers.

1. n=40, p = .2
So, Mean = 40*.2 = 8
Histogram D has mean of 8 as it is symmetrical/centered on 8

2. n=30, p=.4
Mean = np = 30*.4 = 12
Histogram A is correct as it' peak is almost at ~12

3. n = 40, p=.5
Mean =np = 40*.5 =20
So, Histogram B is correct as it is symmetrical at 20.

4. n=100, p=.7
Mean =np = 100*.7 =70
So, Histogram C is correct as it is symmetrical at 70.

5. n=30, p=.9
Mean =np = 30*.9 =27
So, Histogram E is correct as it is symmetrical (almost) at 27

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