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Sam has 6 rose bushes. He counted the flowers on each of them. There are 8, 2, 5, 4, 11 and 9. Find the Standard Deviation. Is X a “Usual” number of flowers? X is your last two digits of your CUNYFirst ID Number. (00 = 0, 01 = 1, …) (20 points) my id is 25
A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 9 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.
A company manufactures bulbs. The probability of getting a defective bulb is 0.055. A sample of 100 bulbs were selected. Use Poisson approximation to binomial distribution to find the probability of finding at most 3 non-defective bulbs.
Two machines P and Q are used to produce bags of cement of masses in kilogrammes shown in the table.
Machine P
50
51
48
50
51
52
54
51
51
Machine Q
54
49
56
47
50
51
52
53
Test if there is a difference between the two machines.
The probability that a life bulb will have a life time of more than 682 hours is 0.9788. The probability that a bulb will have a life time of more than 703 hours is 0.0051. Find the probability that a bulb will last for more than 648 hours.
The mean and variance of defective items is 0.72 and 0.6876. Find the probability of getting 12 non-defective items.
The table given below is for scores in Management Accounting M.A) and Quantitative Techniques (Q.T).
Student
A
B
C
D
E
F
G
H
M.A
86
77
68
71
67
90
78
71
Q.T
80
82
73
69
72
85
84
65
Test for existence of linear relationship at 5% level of significance.
A travel agency receives an average of 150 calls per hour (time between calls are exponentially distributed). It takes an operator an average of 5 minutes to handle a call (exponentially distributed). If a caller gets a busy signal, the travel agency assumes that he or she will call a competitor, and the travel agency will lose an average of $50 in profit. The cost of keeping a phone line open is $12 per hour. How many operators should the travel agency have on duty?
A store donated a lot of 8 computer sets that includes 3 which are malfunctioning or defective. If 4 of this computer sets are chosen at random for delivery to a school.
i) What will be the probability mass function of a random variable 𝑌?
ii) What will be the expected value of 𝑌?
For each fixed λ > 0, let X have a Poisson distribution with parameter λ. Suppose λ
itself is a random variable with the gamma distribution
f(λ) =
1
Γ(n)
λ
n−1
e
−λ
, λ ≥ 0
0, λ < 0
where n is a fixed positive constant. Show that
P(X = k) = Γ(k + n)
Γ(n)Γ(k + 1)
1
2
k+n
, k = 0, 1, 2
