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Attached is a dataset that lists estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men from K.W. Penrose, A.G. Nelson, A.G. Fisher, FACSM, Human Performance Research Center, Brigham Young University, Provo, Utah 84602 as listed in Medicine and Science in Sports and Exercise, vol. 17, no. 2, April 1985, p. 189.
1. Attendance at Orlando’s newest Disneylike attraction, Lego World, has been as follow:
QUARTER
GUEST (IN THOUSADS)
QUARTER
GUEST (IN THOUSADS)
Winter Year 1
73
Summer Year 2
124
Spring Year 1
104
Fall Year 2
52
Summer Year 1
168
Winter Year 3
89
Fall Year 1
74
Spring Year 3
146
Winter Year 2
65
Summer Year 3
205
Spring Year 2
82
Fall Year 3
98
a) Compute the Seasonal Indices using all the data.
b) If the expected guest for the next year (i.e., Forth Year) is 550000, forecast the quarterly attendance for the year 4?
1. Income at the architectural firm Spraggins and Yunes for the period February to July was as follows:
MONTH
FEBRUARY
MARCH
APRIL
MAY
JUNE
JULY
Income (in RM thousand)
70.0
68.5
64.8
71.7
71.3
72.8
Use trend-adjusted exponential smooting to forecast the firm’s August income. Assume February is RM65,000 and the initial trend adjustment is 0. The smooting constants selected are α = 0.1 and β = 0.2.
Question 3. A tire manufacturer warranties its tires to last at least 20,000 miles or “you get a new set of tires.” In its experience, a set of these tires lasts on average 26,000 miles with a standard deviation of 5,000 miles. Assume that the wear is normally distributed. The manufacturer profits $200 on each set sold, and replacing a set costs the manufacturer $400.
(a) What is the probability that a set of tires wears out before 20,000 miles?
(b) What is the probability that the manufacturer turns a profit on selling a set to one customer?
(c) If the manufacturer sells 500 sets of tires, what is the probability that it earns a profit after paying for any replacements? Assume that the purchases are made around the country and that the drivers experience independent amounts of wear.
Consider the following probability density function:
fX(x)=kx 0<=x<2,
=k(4-x), 2<=x<=4
=0, otherwise
a) Find the value of k for which fX(x) is a valid probability density function.
b) Find the mean of X.
c) Find and skecth the probability distiribution function FX(x).
AB and CD are two lines of length 10 cm. and 5 cm. respectively.
We choose point P on line AB and point Q on line CD at random.
Length of CQ=X and length of AP=Y are two independent random variable
a) P(Y > X)=?
b) P( X=2. Y=2)=?
Probability density function of random variable X is given as:
"f(x)=0.4&*(x+4)+0.2[u(x+3)-u(x+2)]+A*e^(-x)*u(x)"
where u(x) is the unit step function.
a) Find and sketch probability distribution function FX(x).
b) Calculate the following probabilities.
P(X=3)
P(-4 ≤ X < -2)
P(-4 < X < -2)
P(X >-4)
P(X < 0)
Assume that in a crowded class, on average 3 students attempt to cheat in any given exam. For a course which will have 2 midterms and 1 final exam in each semester, what is the probability that there will be less than 5 cheating attempts in this course’s exams for any given semester?
For 80% of lectures, Professor John Smith arrives on time and starts lecturing with delay T. When Professor is late, the starting time delay T is uniformly distributed between 0 and 300 seconds. Find the probability distiribution and probability density function of random variable T.
Many college and university students
obtain summer jobs. A statistics professor wanted
to determine whether students in different degree
programs earn different amounts. A random sample
of 5 students in the B.A., B.Sc., and B.B.A. programs
were asked to report what they earned the
previous summer. The results (in $1,000s) are listed
here. Can the professor infer at the 5% significance
level that students in different degree programs differ
in their summer earnings?
B.A. B.Sc. B.B.A.
3.3 3.9 4.0
2.5 5.1 6.2
4.6 3.9 6.3
5.4 6.2 5.9
3.9 4.8 6.4
#340153 on Dec 2023