X is a exponentially distributed random variable with a mean of 10. Use Excel to

Question

X is a exponentially distributed random variable with a mean of 10. Use Excel to calculate the following: a. P(x lessthanorequalto 15) b. P(8 lessthanorequalto x lessthanorequalto 12) c. P(x greaterthanorequalto 8) The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 5 minutes. a. What is the probability density function for the time it takes to change the oil? b. What is the probability that it will take a mechanic less than 6 minutes to change the oil? c. What is the probability that it will take a mechanic between 3 and 5 minutes to change the oil?

Explanation / Answer

For the given case X is a continues random variable as time measured.

We are given that m = 10

Part a)

We need to find P ( x 15)

Before going for calculation we must know q ( decay parameter ).

We know that:

q = 1 / m

= 1/10 = 0.10

X ~ Exp ( q )

The probability density function is : f ( X ) = q e -qx

P ( X < x ) = 1 - e-qx

For exponential function we use excel formula:

=1-EXP(-15*0.1)

=0.7769

Answer: 0.7769

Part b)

P (8 x 12)

=(1-EXP(-12*0.1))-(1-EXP(-8*0.1))

=0.1481

Answer: 0.1481

Part c)

P (x 8 ) = e-qx

=EXP(-8*0.1)

= 0.4493

Answer: 0.4493

Related Questions

Navigate

• Browse (All)
• Browse X
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.