Question

the event that y takes on the value 5 can be represented as {y = 5}.
the event that y takes on a value less than 5 can be represented as {y < 5}.
the event that y takes on a value of at least 5 can be represented as {y ≥ 5}.
c. find p(y = 5), p(y < 5), and p(y ≥ 5).
p(y = 5) = .6 (type an integer or a decimal. do not round.)
p(y < 5) = .2 (type an integer or a decimal. do not round.)
p(y ≥ 5) = .8 (type an integer or a decimal. do not round.)
d. construct a probability histogram for the random variable y. choose the correct histogram below.
a.
b.
c.
d.

Explanation:

Step1: Analyze the probabilities

We know that \(P(Y = 5)=0.6\), \(P(Y<5)\) is the sum of probabilities for \(Y = 3\) and \(Y = 4\). Let \(P(Y = 3)=0.1\) and \(P(Y = 4)=0.1\), so \(P(Y<5)=0.1 + 0.1=0.2\). And \(P(Y\geq5)=P(Y = 5)+P(Y = 6)\). Since \(P(Y<5)+P(Y\geq5)=1\), and \(P(Y<5) = 0.2\), then \(P(Y\geq5)=1 - 0.2=0.8\).

Step2: Match with the histogram

In option A, the bar for \(Y = 5\) has a relatively large probability (0.6), the sum of bars for \(Y<5\) ( \(Y = 3\) and \(Y = 4\)) is 0.2, and the bar for \(Y\geq5\) ( \(Y = 5\) and \(Y = 6\)) has a probability of 0.8.

Answer:

A.