Suppose Brandi buys a CD for $1000 that earns 3% APR and is compounded
2 answers:
Answer:
$1,061.76
Step-by-step explanation:
(refer to attached handout)
For compound interest, you are given:
A = ? (need to find)
P = $1000
r = 3% = 0.03
n = compounded monthly = 12 times per year
t = 2 years
(substituting this into the formula)
A = P [ 1 + (r/n) ] ^(nt)
A = 1000 [ 1 + (0.03/12) ] ^[(12)(2)]
A = 1000 [ 1 + 0.0025 ] ^24
A = 1000 [ 1.0025 ] ^24
A = 1,061.76
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Answer:
(a) P(X 20) = 0.9319
(b) Expected number of defective light bulbs = 15
Step-by-step explanation:
We are given that a manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random.
Firstly, the above situation can be represented through binomial distribution, i.e.;
where, n = number of samples taken = 150
r = number of success
p = probability of success which in our question is % of bulbs that
are defective, i.e. 10%
<em>Now, we can't calculate the required probability using binomial distribution because here n is very large(n > 30), so we will convert this distribution into normal distribution using continuity correction.</em>
So, Let X = No. of defective bulbs in a box
<u>Mean of X</u>, =
=
= 15
<u>Standard deviation of X</u>, =
=
= 3.7
So, X ~ N(
Now, the z score probability distribution is given by;
Z = ~ N(0,1)
(a) Probability that this box will contain at most 20 defective light bulbs is given by = P(X 20) = P(X < 20.5) ---- using continuity correction
P(X < 20.5) = P( <
) = P(Z < 1.49) = 0.9319
(b) Expected number of defective light bulbs found in such boxes, on average is given by = E(X) = =
= 15.