A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables. For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.

The random variable X is also a Poisson random variable because it represents the fixed number of students arriving at the 10:30 AM time slot.

The random variable X follows a Poisson distribution with parameter λ = 3.

The probability mass function of X is given by:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...,\ \lambda>0$

Compute the probability of X = 2 as follows:

$P(X=2)=\frac{e^{-3}3^{2}}{2!}=\frac{0.0498\times 9}{2}=0.2241$

Thus, the probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.

6 0

3 years ago

Read 2 more answers

The National Assessment of Educational Progress (NAEP) gives a math assessment every year to 12th graders in the U.S. On the mat

amid [387]

Answer:

The correct answer is option 2.

Step-by-step explanation:

In this case we need to test whether young men nationwide have a mean score below 275 in the National Assessment of Educational Progress math assessment.

The hypothesis is defined as follows:

H₀: μ = 275 vs. Hₐ: μ < 275

The significance level of the test is α = 0.05.

The p-value of the test is computed as, p-value = 0.20.

Decision rule:

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard the null hypothesis.

A large p-value (> 0.05) specifies fragile proof against the null hypothesis, so you fail to discard the null hypothesis.

p-value = 0.20 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.

Thus, it can be concluded that there is not enough evidence to conclude that the mean score is less than 275 for young men nationwide.

Thus, the correct answer is option 2.

5 0

3 years ago

What is the measure of x?

tankabanditka [31]

Answer:

Step-by-step explanation:

half of 67 i believe its correct

3 0

3 years ago