What is 10% of 10? Round to the nearest hundredth (if necessary).

If N = , r = , and n = , and assuming that X has a hypergeometric probability distribution, compute the following. Write your an

artcher [175]

Answer:

(a) The value of P (X = 2) is 0.3571.

(b) The value of P (X ≤ 1) is 0.5952.

Step-by-step explanation:

A Hypergeometric distribution is used to describe the probability distribution of x successes in n random draws from a population of size N that contains exactly r items that are considered as success. In this distribution each draw results in either a success or a failure.

The probability mass function of Hypergeometric distribution is:

$P(X=x)=\frac{{r\choose x}{N-r\choose n-x}}{{N\choose n}}$

Given:

N = 9

r = 3

n = 4

(a)

Compute the value of P (X = 2) as follows:

$P(X=2)=\frac{{3\choose 2}{9-3\choose 4-2}}{{9\choose 4}}=\frac{3\times 15}{126}=0.3571$

Thus, the value of P (X = 2) is 0.3571.

(b)

Compute the value of P (X ≤ 1) as follows:

P (X ≤ 1) = P (X = 0) + P (X = 1)

$=\frac{{3\choose 0}{9-3\choose 4-0}}{{9\choose 4}}+\frac{{3\choose 1}{9-3\choose 4-1}}{{9\choose 4}}\\=0.1190+0.4762\\=0.5952$

Thus, the value of P (X ≤ 1) is 0.5952.

4 0

3 years ago

The height above the ground attained by a football (in feet) after it is kicked is given by the equation h(t) = -16t^2 +32t, whe

Damm [24]

Answer:

A. The ball returns to the ground 2 seconds after it was kicked.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

In how many ways can 8 diplomats be seated at a round table? A)40,320 B)5,040 C)720

Tanzania [10]

Answer:

B)5,040

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.7 millimeters and a standard deviati

slava [35]

Answer:

The diameter that separates the top 3% is of 5.85 millimeters, and the one which separates the bottom 3% is of 5.55 millimeters.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

$Z = \frac{X - \mu}{\sigma}$

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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.7 millimeters and a standard deviation of 0.08 millimeters.

This means that $\mu = 5.7, \sigma = 0.08$