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A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that 75% of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. On a certain day, eight customers bought it for the first time. Find the probability that at least six of the eight customers will like this hamburger
If the duration of kidney disease from the onset of symptoms until kidney “failure” ranges from 1 to 5 years, the average is 2.42 years with a standard deviation of 0.89 years. One administrator of a public medical center randomly selected the medical records of 41 patients with damaged kidneys. Find the probability for :
1. the average duration is less than 3.2 years.
2. the average duration exceeds 3.2 years.
3. the average duration lies within 0.8 year of the population mean
Prince wants to open a Hair Salon and asks his uncle Lerumo if he wil l lend him the money. He also indicates that he wil l only be able to start paying him back after five years, at which time he wil l then pay R35 000 at the end of every four months, for four years. Uncle Lerumo agrees, on condition that his money must earn 12,2% interest per year,compounded every four months
1.The present value of Prin e's debt when he starts paying ba k un le Lerumo after 5 years will be?
2.The amount that Unc le Lerumo lends Prince is?
A person’s blood glucose level and diabetes are closely related. Let x be a random variable measuring the glucose in mg per decilitre of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean µ = 85 and standard deviation σ = 25. (Source: Diagnostic Tests with Nursing Implications, edited by S. Loeb, Springhouse Press). Note: after 50 years of age, both the mean and standard deviation tend to increase.
(a) What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is less than 60?
(b) What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is between 70 and 100?
(c) What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is more than 125? (borderline diabetes starts at 125)
(d) Find the minimum glucose level (after a 12-hour fast) required to participate in a study reserved for the top 10% of people.
Let X and Y be independent random variables each having a geometric probability
mass function with parameter 1/2 Let Z = Y - X and M = min(X, Y) . Find the joint
p.m.f of M and Z P(M=m , Z=z) , for integers z and m > 0
The present value of an annuity is R62 543,42. The time under Consideration is 10 years and the applicable interest rate is 16% per year, compounded monthly. The future value of this annuity is
1. R162 612,89.
2. R1 333 517,61.
3. R306 521,61.
4. R581 913,00.
Given that the variance is Q, determine the standard deviation in terms of Q.
a) 0.5Q
b) 2Q
c) Q
d) Q2
The Boxing Fund must pay Daniel an old boxer, R18 000 every three months indenitely compensation.
Money is worth 11,4% per year,
ompounded quarterly.
1. What is the opening balance on this investment fund?
sketch the astroid in curves also calculate its tangent vector at each point .at which point is the tangent vector zero:
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
The distance between the centers of the two gears is 20
cm . The shaft of each gear is 5 cm and 9 cm respectively.
A. What are the central angles of the shafts
on the gears?
B. What is the length of the arc length part
of the belt?
C. What is the length of the non-contacting part of the belt?
D. What is the total length of the belt?
