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Chapter 5: Q. 5.1 (page 217)

The number of minutes of playing time of a certain high school basketball player in a randomly chosen game is a random variable whose probability density function is given in the following figure:

Find the probability that the player plays

(a) more than 15minutes;

(b) between 20and35minutes;

(c) less than 30minutes;

(d) more than 36minutes

Short Answer

Expert verified

(a) The probability that the player plays more than 15minutes is 0.875

(b) The probability that the player plays between 20and35is 0.625

(c) The probability that the player plays less than30minutes is0.75

(d) The probability that the player plays more than36minutes is0.1

Step by step solution

01

Find the probability that the player plays more than 15 minutes (part a)

Formalize the given probability function. As may be observed from the graph,

f(x)=0.025,x鈭�[10,20)鈭�(30,40]

f(x)=0.05,x鈭�[20,30]

f(x)=0, otherwise

Xis the random variable with the density function defined P. The needed probabilities are calculated as the integrals of the density function fover the relevant intervals.

P(X>15)=1-P(X鈮�15)=1-鈭�1015f(x)dx=1-鈭�10150.025dx

=1-0.025脳5=0.875

02

Find the probability that the player plays between 20 and 35 minutes (part b)

P(X鈭�(20,35))=P(X鈭�(20,30))+P(X鈭�(30,35))

=鈭�2030f(x)dx+鈭�3035f(x)dx

=0.05脳10+0.025脳5=0.625

03

Find the probability that the player plays less than 30 minutes (part c)

P(X<30)=1-P(X鈮�30)=1-鈭�3040f(x)dx=1-鈭�30400.025dx

=1-0.025脳10=0.75

04

Find the probability that the player plays more than 36 minutes (part d)

P(X>36)=鈭�3640f(x)dx=鈭�36400.025dx=0.025脳4=0.1

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