Suppose that about 55% of the people who are murdered actually knew the person who committed the murder. Suppose that a detective file in Boston has 51 current unsolved murders. What is the probability that fewer than 21 victims did not know their murderer?

24.51% probability that fewer than 21 victims did not know their murderer

Step-by-step explanation:

I am going to approximate the binomial probability distribution to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that , .

In this problem, we have that:

So

What is the probability that fewer than 21 victims did not know their murderer?

That is, more than 30 knew the murdered.

, which is 1 subtracted by the pvalue of Z when X = 30.5. So

has a pvalue of 0.7549

1 - 0.7549 = 0.2451

24.51% probability that fewer than 21 victims did not know their murderer

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50

answer: the correct one is a

step-by-step explanation: