Hello! i need help with question 67 & 68
1 answer:
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Answer:
(a) P(X = 4) = 0.0189
(b) P(X 4) = 0.9919
(c) P(X 4) = 0.027
Step-by-step explanation:
We are given that the probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.7 .
Since we have to find the probabilities for 1st successful alignments, so the probability distribution that we will use here is Geometric distribution.
<u>Geometric distribution</u> is used when we are interested in knowing the chances of our first success.
The probability distribution of geometric distribution is given by;
where, = number of trials
k = first success = 1
p = probability of getting success = 0.70
So, X ~ Geo(p = 0.7)
(a) Probability that the 1st successful alignment requires exactly 4 trials is given by = P(X = 4)
Here, = 4, p = 0.7 and k = 1
So, P(X = 4) = =
= 0.0189
(b) Probability that the 1st successful alignment requires at most 4 trials is given = P(X 4)
P(X 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
=
=
= 0.7 + 0.21 + 0.063 + 0.0189 = 0.9919
(c) Probability that the 1st successful alignment requires at least 4 trials is given by = P(X 4)
P(X 4) = 1 - P(X < 4) = 1 - P(X
3)
P(X 4) = 1 - P(X = 1) - P(X = 2) - P(X = 3)
=
=
= 1 - 0.7 - 0.21 - 0.063 = 0.027
1. the formula for the slope is
where (a,0) is x1, y1 and (0,2a) is x2, y2. try to see if you can do it now (:
2. take a number x, then step by step do whatever the question asks for example "First, 3 is subtracted from x" so you know the first thing you need to do is x-3, then go on and you'll get an equation which you can use to solve for x, try it!
3. make a set, S, which has multiples of 7. then make a set, T, which has multiples of 13.
now the intersection of S and T is a set having all elements of S, also found in T (basically the numbers that are common to both). try doing it now!
for fourth, this requires a profit formula(that I do not know), must be explained in your book, try going over it, I'm sure you'll find it there!
where (a,0) is x1, y1 and (0,2a) is x2, y2. try to see if you can do it now (:
2. take a number x, then step by step do whatever the question asks for example "First, 3 is subtracted from x" so you know the first thing you need to do is x-3, then go on and you'll get an equation which you can use to solve for x, try it!
3. make a set, S, which has multiples of 7. then make a set, T, which has multiples of 13.
now the intersection of S and T is a set having all elements of S, also found in T (basically the numbers that are common to both). try doing it now!
for fourth, this requires a profit formula(that I do not know), must be explained in your book, try going over it, I'm sure you'll find it there!