Homework Answers

11. Find z if the standard normal-curve area

a) between 0 and z is 0.4726;

b) to the left of z is 0.9868;

c) to the left of z is 0.3085;

d) between -z and z is 0.9282

12. If a random variable has the normal distribution with \mu = 82:0 and

\sigma = 4:8, nd the probabilities that it will take on a value

a) less than 89.2;

b) greater than 78.4;

c) between 83.2 and 88.0;

d) between 73.6 and 90.4.

13. If the time to assemble an \easy to assemble" computer desk from a

kit is a random variable having the normal distribution with \mu = 55:8

minutes and \sigma = 12:2 minutes, what are the probabilities that this

kind of desk can be assembled in

a) less than 49.7 minutes;

b) anywhere from 61.9 and 74.1 minutes;

c) more than 86.3 minutes?

14. With reference to Exercise 13, for what length of time is the probability

0.90 that one can assemble the desk in that many minutes or less?

Find number of students securing marks >104, between 155-165, <55 from the following class data.

Class(marks) frequency (students)

0-20 210

20-40 115

40-60 130

60-80 220

80-100 120

100-120 101

120-140 120

140-160 144

160-180 132

180-200 190

2. A company purchased machinery that cost 510,000. It is estimated that the machine will be operated for 100,000 hours over its useful life and have a residual value of 10,000.

Required:

A) what is the rate of depreciation per hour?

B) journalize the entry for annual depreciation if the machine had been operated for 22,000 hours?

How to find the coordinate of p and q if the circle cuts the x-axis at the points p and q in 2x^2 +2y^2 -8x +5y -10=0

5. A class in statistics contains 10 students, 3 of whom are 19, 4 are 20, 1

is 21, 1 is 24, and 1 is 26. Let X be the average age of the 2 randomly

selected students and derive the probability function for X.

6. A man has four keys in his pocket and, since it is dark, cannot see which

is his door key. He will try each key in turn until he finds the right one.

Let X be the number of keys tried (including the right one) to open the

door. What is the probability function for X?

7. Suppose a fair die is tossed two times. Let X be the larger of the two

faces that appear. Find px(k).

8. Suppose a particle moves along the x-axis beginning at 0. It moves one

integer step to the left or right with equal probability. What is the probability

function of its position after four steps?

9. Five cards are dealt from a standard 52-card deck. Let Y be the number

of red cards that are dealt. What is the probability function for Y ?

{Fs} The equation for a displacement 𝑠(𝑚), at a time 𝑡(𝑠) by an object starting at a displacement of 𝑠0 (𝑚), with an initial velocity 𝑢(𝑚𝑠 −1 ) and uniform acceleration 𝑎(𝑚𝑠 −2 ) is: 𝑠 = 𝑠0 + 𝑢𝑡 + 1 2 𝑎𝑡 2 A projectile is launched from a cliff with 𝑠0 = 30 𝑚, 𝑢 = 55 𝑚𝑠 −1 and 𝑎 = −10 𝑚𝑠 −2 . The tasks are to: a) Plot a graph of distance (𝑠) vs time (𝑡) for the first 10s of motion. b) Determine the gradient of the graph at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. c) Differentiate the equation to find the functions for: i) Velocity (𝑣 = 𝑑𝑠 𝑑𝑡) ii) Acceleration (𝑎 = 𝑑𝑣 𝑑𝑡 = 𝑑 2 𝑠 𝑑𝑡2 ) d) Use your results from part c to calculate the velocity at 𝑡 = 2𝑠 and 𝑡 = 6𝑠. e) Compare your results for part b) and part d). f) Find the turning point of the equation for the displacement 𝑠 and using the second derivative verify whether it is a maximum, minimum or point of inflection. g) Compare your results from f) with the graph you produced in a).

Find the equation of the line which is perpendicular to 4𝑦=5𝑥−8 and passing through (2,3).

A random sample of size 16 has 53 as mean. The sum of the squares of the deviation

taken from mean is 150. Can this sample be regarded as taken from the population having

56 as mean? Obtained 95% and 99% level of confidence limit of the mean of population

The line 𝑦=𝑥−5 is tangent to the curve 𝑦=𝑥^2−9𝑥−𝑘

Find the value of 𝑘.