Suppose that a continuous random variable takes on values on the interval from 0

Question

Suppose that a continuous random variable takes on values on the interval from 0 to 2 and that the graph of its probability density is as shown in Figure R.1. What are the probabilities that the random variable will take on a value (a) less than 0.5; (b) between 1.2 and 1.6? The manager of an ambulance service knows that the number of emergency calls by the ambulances each day is a random variable approximately a normal distribution with the mean 36.2 and the standard deviation = 5.1. What are the probabilities that in any given day the ambulance service will make (a) exactly 30 emergency ambulance service calls; (b) at most 30 emergency ambulance service calls? (Note that this is a whole number which requires a continuity correction.)

Explanation / Answer

Q91

the pdf of a given continuous distribution is

f(x)= x for x in [0,1]

= 2-x for x in [1,2]

a) P(X<0.5) = integration(from=0, to=0.5)f(x)dx #

= 0.125

b) P(1.2<X<1.6)= integration(from=1.2, to=1.6)f(x)dx ## f(x) =2-x

P(1.2<X<1.6) =0.24

Q.92

The number of emergency calls made by ambulance each day is a random sample distributed with mean= 36.2

and standard deviation = 5.1

a) The probability that the ambulance service will make exactly 30 emergency calls

i.e. P(X=30) =0 ## since the distribution is continuous the probability of taking specific value is zero.

b) The probability that the ambulance service will make atmost 30 emergency calls

i.e. P(0<X<30)= 0.11205 ## by suing command ## pnorm(30,36.2,5.1)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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