Statistics and Probability Answers

Lorry carries heavy Cartons of Goods. The weights of these cartons are distributed about a mean of 100kg and with a standard deviation of 7kg. Find how many cartons the Lorry can carry so that the probability of the total load exceeding 4500kg is less than 0.05.

The weights of the packages received by a department store have a mean of 300 lb and a standard deviation of 50 lb. What is the probability that 25 packages received at random and loaded on an elevator will exceed the safety limit of the elevator, listed as 8,200 lb?

Ball bearings of a given brand weigh 0.5 oz with a standard deviation of 0.02 oz. What is the probability that two lots of 1,000 ball bearings each, will differ in weight by more than 2 oz?

A company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $150.

If they offer a 2 year extended warranty for $19, what is the company's expected value of each warranty sold?

The heights of 500 students are normally distributed with a mean of 144.5 centimeters and a variance of 36 centimeters. Assuming that the
heights are recorded to the nearest half-centimeter,
find probability,
(a) less than 130.0 centimeters?
(b) between 151.5 and 182.0 centimeters inclusive?
(c) greater than or equal to 150.0 centimeters?
(d) p(x>x0)=0.6

The heights of 500 students are normally distributed with a mean of 144.5 centimeters and a variance of 36 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, find the Probability.
(a) Less than 130.0 centimeters?
(b) Between 151.5 and 182.0 centimeters inclusive?
(c) Greater than or equal to 150.0 centimeters?
(d) P(x > x0) = 0.6

The height of the students in a certain class is following normal distribution with mean

height as 165 cm and standard deviation of 25 cm. There are 60 students in that class.

Determine

i. The number of students whose height is more than 158 cm

ii. The number of students whose height is lying between 155 and 172 cm.

3. b. Find the lowest height among the tallest 5 student in a class.

In a lottery game, a player picks six numbers from 1 to 27. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.

What is the expected value of this game? $

A jar contains 10 red marbles numbered 1 to 10 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event.

(a) The marble is red
Your answer is :
10
18​Correct

(b) The marble is odd-numbered
Your answer is :
9
18​Correct

(c) The marble is red or odd-numbered
Your answer is :

(d) The marble is blue or even-numbered
Your answer is :

Regress the sales volume on #household, number of cars and marketing expense.
Calculate R square and interpret the same.
iii. Determine which variable is/are significant variable/s. Is there any insignificant
variable? If yes, regress again, by dropping the variable. Will dropping that variable
increases the adjusted R square?