The price of a laptop of a particular make and configuration among dealers natio

Question

The price of a laptop of a particular make and configuration among dealers nationwide is assumed to have a normal distribution with mean µ = $1200 and standard deviation = $50.

(a) What is the probability that a laptop of the same make, chosen randomly from a dealer, will cost less than $1100?

(e) What is the probability that the average price of 25 laptops of the same make, chosen randomly from a dealer, will be greater than $1225?

(f) Compute the probability that at least 4 out of 5 laptops of the same make picked randomly will cost less than $1100? (Hint: Use the binomial random variable with success probability in Part (a).)

Explanation / Answer

The price of a laptop of a particular make and configuration among dealers nationwide is assumed to have a normal distribution with mean µ = $1200 and standard deviation = $50.

(a) What is the probability that a laptop of the same make, chosen randomly from a dealer, will cost less than $1100?

Z value for 1100, z=(1100-1200)/50 =-2

P( x <1100)= P( z < -2) = 0.0228

(e) What is the probability that the average price of 25 laptops of the same make, chosen randomly from a dealer, will be greater than $1225?

Standard error = sd/sqrt(n) =50/sqrt(25) =10

Z value for 1225, z=(1225-1200)/10 =2.5

P( x >1225)= P( z >2.5) = 0.0062

(f) Compute the probability that at least 4 out of 5 laptops of the same make picked randomly will cost less than $1100? (Hint: Use the binomial random variable with success probability in Part (a).)

p=0.0228

n=5

P(X = 4) = 0.000001320361

P(X = 5) = 0.000000006161

P( x 4) =P( x=4)+P( x=5)

=0.000001320361+0.000000006161

=0.000001326522

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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