Consider a disease whose presence can be identified by carrying out a blood test. Let p denote the probability that a randomly selected individual has the disease. Suppose n individuals are independently selected for testing. One way to proceed is to carry out a separate test on each of the n blood samples. A potentially more economical approach, group testing, was introduced during World War II to identify syphilitic men among army inductees. First, take a part of each blood sample, combine these specimens, and carry out a single test. If no one has the disease, the result will be negative, and only the one test is required. If at least one individual is diseased, the test on the combined sample will yield a positive result, in which case the n individual tests are then carried out. [The article "Random Multiple-Access Communication and Group Testing"† applied these ideas to a communication system in which the dichotomy was active/idle user rather than diseased/nondiseased.] If p = 0.15 and n = 5, what is the expected number of tests using this procedure? (Round your answer to three decimal places.)

Answers

Answer 1

Answer:

Answer:

The expected number of tests, E(X) = 6.00

Step-by-step explanation:

Let us denote the number of tests required by X.

In the case of 5 individuals, the possible value of x are 1, if no one has the disease, and 6, if at least one person has the disease.

To find the probability that no one has the disease, we will consider the fact that the selection is independent. Thus, only one test is necessary.

Case 1: P(X=1) = [P (not infected)]⁵

= (0.15 - 0.1)⁵

P(X=1) = 3.125*10⁻⁷

Case 2: P(X=6) = 1- P(X=1)

= 1 - (1 - 0.1)⁵

P(X=6) = (1 - 3.125*10⁻⁷) = 0.999999

P(X=6) = 1.0

We can then use the previously determined values to compute the expected number of tests.

E(X) = ∑x.P(X=x)

= (1).(3.125*10⁻⁷) + 6.(1.0)

E(X) = E(X) = 6.00

Therefore, the expected number of tests, E(X) = 6.00

The answer is $4a(16a^2+27b^2)-3b(9b^2+48b)$

Step-by-step explanation:

step one:

let us re-write the expression in mathematical terms for clarity

we have the expression stated below

$64a^3-27b^3-144b^2+108ab^2$

step two:

We are going to collect like terms before factorization we have

$64a^3+108ab^2-27b^3-144b^2$

We can now factorize the expression we have

$4a(16a^2+27b^2)-3b(9b^2+48b)$

If x-13 = k and k = 3, what is the value of x?

Answers

Answer:

x = 16

16 - 13 = 3

***brainliest please

Step-by-step explanation:

What property allows us to determine the congruency of the two triangles in the diagram?A. SSS
B. ASA
C. HL
D. SAS

Answers

A. SSS

That is because the diagram only shows that the sides are congruent and does not show anything else. (Like angles or anything)

The correct answer is A.SSS.

P.S. I am only answering this question so you could give the brainliest to the person who answered first :)

Scores on a test in a very large class are bell-shaped and symmetric. The mean on the test was 75, and the standard deviation was 5. What percent of the scores were above 75?

Answers

Answer:

50% of the scores were above 75

Step-by-step explanation:

Problems of normally distributed(bell-shaped) samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 75, \sigma = 5$