For question one, refer to the table below which describes the numbers of adults

Question

For question one, refer to the table below which describes the numbers of adults in groups of five who reported sleepwalking.

x 0 1 2 3 4 5

P(x) 0.172 0.363 0.306 0.129 0.027 0.003

a. Find the mean for the number of sleepwalkers in groups of five and explain what it means in a complete sentence.

b. Find the probability of getting exactly 2 sleepwalkers among 5 adults.

c. Find the probability of getting at least 3 sleepwalkers among 5 adults.

d. Find the probability of getting at most 4 sleepwalkers among 5 adults.

Explanation / Answer

a.

f= 1

fx = 1.485

Mean = fx / f = 1.485

Mean square = f x^2 / f = 3.255

Variance = (Mean square) - (Mean)^2

Variance = f x^2 - Mean^2 = 1.05

Stadard Dev= Var = 1.025

b.

the probability of getting exactly 2 sleepwalkers among 5 adults P(X=2)= 0.306

c.

the probability of getting at least 3 sleepwalkers among 5 adults= =P(X=3)+P(X=4)+P(X=5)=0.129+0.027+0.003

=0.159

d.

the probability of getting at most 4 sleepwalkers among 5 adults

=P(X=0)+P(X=1)+P(X=2)+P(X=4)

=0.172+0.363+0.306+0.129+0.027

=0.997

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.172 0 0 0 1 0.363 0.4 1 0.363 2 0.306 0.6 4 1.224 3 0.129 0.4 9 1.161 4 0.027 0.1 16 0.432 5 0.003 0 25 0.075

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