Question

If possible, please explain how to do using a Ti-84 calculator, or workout all calculations.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About 62% of people who are murdered actually knew the person who committed the murder.† Suppose that a detective file in New Orleans has 58 current unsolved murders. Find the following probabilities. (Round your answers to four decimal places.)

(a) at least 35 of the victims knew their murderers Incorrect: Your answer is incorrect.

(b) at most 48 of the victims knew their murderers

(c) fewer than 30 victims did not know their murderers

(d) more than 20 victims did not know their murderers

Answer 1

p = 0.62 , n= 58

mean = np = 58 * 0.62 = 35.96

sd =sqrt( np q) = sqrt(58*0.62 * 0.38) = 3.6966

Z = (X - mean)/sd

=(X - 35.96)/3.6966

X = number of person who knew the person who committed the murder

a)

P(X >= 35)

= P(X >= 34.5)

=P (Z>−0.39)

=0.6517

b)

P(X <= 48)

= P(X <= 48.5)

= P (Z<3.39)

= 0.9997

c)

fewer than 30 who did not know their murderers

= more than or equal to 58-30 = 28

P(X >= 28)

=P(X > 28.5)

= P (Z>−2.02)

=0.9783

d)

more than 20 who did not know their murderers

= less than or equal to 58-20 = 38

P(X <= 38)

= P(X <= 38.5)

=P (Z<0.69)

=0.7549