# Math

On a certain road 20% of the vehicles are trucks, 16% are buses and the remainder are cars.
(i) A random sample of 11 vehicles is taken. Find the probability that fewer than 3 are buses. [3]
(ii) A random sample of 125 vehicles is now taken. Using a suitable approximation, find the
probability that more than 73 are cars.

1. 👍
2. 👎
3. 👁
1. A truck driver estimates that a country road rises 40 cm for every 6 m along the road. What is the angle of inclination of the road?

1. 👍
2. 👎
2. solution, P(X < 3) = P(0) + P(1) + P(2) M1
Binomial term with 11Cr p

= (0.84)11 + (0.16)(0.84)10 × 11C1 +
(0.16)2
(0.84)9
× 11C2
Correct expression for P(0, 1, 2) or P(0, 1, 2, 3)

= 0.1469 + 0.30782 + 0.2931
= 0.748
ii) μ = 125 × 0.64 = 80
σ^2= 125 × 0.64 × 0.36 = 28.8
P(X > 73) = 1 –phi(73.5-80/sqrt(28.8)
standardising = phi(1.211)
observe region, correct region (> 0.5 if mean > 73.5, if mean < 73.5)
= .887 ans

1. 👍
2. 👎

## Similar Questions

1. ### Statistics

This is a stats problem. Twenty percent of all trucks undergoing a certain inspection will fail the inspection. Assume that trucks are independently undergoing this inspection, one at a time. The expected number of trucks

2. ### Math

The U drive rent a truck company plans to spend 13 million on 320 new vehicles. Each commercial van will cost \$35000, each small truck \$30000, and each large truck \$80000. Past experience shows that they need twice as many vans as

3. ### math

Buses to Aintree leave the station every 25 minutes. Buses to Blossford leave the station every 30 minutes. Buses to both places leave at 8am. What is the next time buses to Aintree and Blossford leave the station together?

4. ### ashford university

Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty

1. ### Calculus

Two trucks start from the same point. One truck travels due east at a rate of 50 mph and the other trucks travels due north at a rate of 60 mph. At what rate is the distance between the two vehicles increasing 1 1/2 hours later? I

2. ### Algebra

A student used synthetic division to divide x^3-x^2-2x by x+1 . This is what the students problem looked like 1_| 1 -1 -2 1 0 ____________ 1 0 -2 answer x remainder -2 a. Describe and correct the error shown. b. Use the Remainder

3. ### maths

Six of the classes at your school are going to the pool for a swimming party. That means 125 students need to get on buses and each bus hold 48 students. How many buses will the school need?

4. ### Math: Fractions

A group charters 3 identical buses and occupies 4/5 of the seats. After 1/4 of the passengers leae, the remaining passangers use only 2 of the busses what fraction of the seats on the two buses are now occupied? assume number of

1. ### Algebra

Evan washes two types of vehicles. It takes him 30 minutes to wash a car and 40 minutes to wash a truck. He charges \$12 to wash a car and \$15 to wash a truck. In 270 minutes, Evan made \$105 washing cars and trucks. How many trucks

2. ### math

The U-Drive Rent-A-Truck company plans to spend \$8 million on 280 vehicles. Each commercial van will cost \$25,000, each small truck \$30,000, and each large truck \$40,000. Past experience shows that they need twice as many vans as

3. ### physics

(a) daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32° ramp at a speed of 4-0.0 m/s (14-4- km/h), How many buses can he clear if the top of the takeoff ramp is at the same

4. ### Algebra 2

"At a school sponsored car wash, the fees charged were: \$5 per car, \$8 per truck, \$10 per van. Twice as many cars were washed as pickup trucks. The amount collected for washing cars and pickup trucks was \$360. A total of \$410 was