Answer:
The probability that X is less than 32 minutes is 0.736.
Step-by-step explanation:
Given : The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 24 minutes.
To find : What is the probability that X is less than 32 minutes?
Solution :
If X has an average value of 24 minutes.
i.e. [tex]\lambda=24[/tex]
The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.
The exponentially function is [tex]\frac{1}{\lambda}e^{-\frac{x}{\lambda}}[/tex]
The function form according to question is
[tex]f(x)=\{\frac{1}{24}e^{-\frac{x}{24}}, x>0\}[/tex]
The probability that X is less than 32 minutes is
[tex]P[x<32]=1-e^{-\frac{32}{24}}[/tex]
[tex]P[x<32]=1-0.26359[/tex]
[tex]P[x<32]=0.736[/tex]
Therefore, the probability that X is less than 32 minutes is 0.736.
