Can someone help me with this question?

Mathematics

1 answer:

vodka [1.7K]2 years ago

8 0

The formula of a rectangular prism is V = lwh, or volume = length times width times height.
If the length is 4 inches, width is 5 inches, and height is 7 inches, then you would just do 4 • 5 • 7 to get the volume.
4 • 5 = 20
20 • 7 = 140
So the volume of this rectangular prism is 140 inches^3.

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4-It has been a bad day for the market, with 70% of securities losing value. You are evaluating a portfolio of 20 securities and

riadik2000 [5.3K]

Answer:

b) 0.0007

c) 0.4163

d) 0.2375

Step-by-step explanation:

We are given the following:

We treat securities lose value as a success.

P(Security lose value) = 70% = 0.7

Then the securities lose value follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 20.

a) Assumptions

There are 20 independent trials.
Each trial have two possible outcome: security loose value or security does not lose value.
The probability for success of each trial is same, p = 0.7

b) P(all 20 securities lose value)

We have to evaluate:

$P(x = 20)\\= \binom{20}{0}(0.7)^0(1-0.7)^{20}\\= 0.0007$

0.0007 is the probability that all 20 securities lose value.

c) P(at least 15 of them lose value.)

$P(x \geq 15)\\= P(x=15) + P(x = 16) + P(x=17) + P(x=18) +P(x = 19) +P(x = 20)\\ \binom{20}{15}(0.7)^{15}(1-0.7)^{5} +...+ \binom{20}{20}(0.7)^{20}(1-0.7)^{0} \\=0.4163$