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If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg?
Question :
The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.
a) Let X be the number of matches that will be won by the team. What are the possible values of X?
b) What is the probability that the team will win exactly 6 matches?
c) What is the probability that the team will lose 2 or less matches?
d) What is the mean number of matches that the team will win?
e) What are the variance and the standard deviation of the number of matches that the team will win?
Doubt in (c) = What is the probability that the team will lose 2 or less matches?
(Here, do we have to use P(X less than equal to 2)?
Let f : A → B be a one-to-one correspondence. By Exercise 3.12, f −1 : B → A is also a one-to-one correspondence. 1. Prove that f −1 ◦ f = iA. 2. Prove that f ◦ f −1 = iB.
A dice is tossed 120 times with the following
results.
Number turned up 1 2 3 4 5 6 Total
Frequency 30 25 18 10 22 15 120
Test the hypothesis that the dice is un biased.
Over a period of time, the number of people leaving a hotel each morning was recorded. These data are
summarised in the stem-and-leaf diagram below:
Stem Leaf Frequency
2 799 3
3 22346 5
4 01489 5
5 2336668 7
6 0145 4
7 23 2
8 1 1
Key: 3 5 = 35. Determine the mode and the median of the data
BrushPro is an one-man paint business owned by Banele. If x offices are painted per month, BrushPro’s
monthly profit, P, is given by the function
P(x) = −x3 + 27x2 + 132x + 2 970,
where 0 ≤ x ≤ 34. Use marginal analysis to determine the approximate change in BrushPro’s monthly profit
when the 23rd office is painted. The profit will
Using weiestrass M-test, show that the following series converges uniformly.
∞
∑n^3X^n,X belongs to[-1/3,1/3]
n=1
A manufacturer estimates that when q units of a certain commodity are produced, the total cost will be
C(x) rand where
C(q) = q2
25 + 80 000 − 104q.
Answer the following questions:
(i) Use marginal analysis to determine the production level at which the cost will be a minimum.
(ii) Determine the minimum cost.
Raggs Limited, a clothing firm, determines that the revenue, in rand, of selling x dresses is given by the
function
R(x) = x(450 − 0,050x).
It also determines that the total cost, in rand, of producing x dresses is given by the function
C(x) = 40 000 + 0,025x2.
The marginal profit when x dresses are produced and sold, is given by the function
A restaurant owner is concerned about the amount of time customers must wait before being served over
weekends. He collects data on the waiting times, to the nearest minute, of 20 tables on Friday evening and
15 tables on Saturday evening.
The average waiting time on Friday evening is 24 minutes per table.
The total waiting time for the 15 tables on Saturday evening is seven hours and three
quarters of an hour.
The mean waiting time per table for Friday and Saturday evening, rounded to the nearest minute, is
#340153 on Dec 2023