10 points 4. Suppose you are dealing with a binomial distribution. Calculate the following probabilities:
a) With 10 trials and a 41 chance of success, the probability of exactly seven successes.
b) With 150 trials and a 39 chance of success, the probability of at least twenty-two successes.

a) 0.048 = 4.8% probability of exactly seven successes.

b) 100% probability of at least twenty-two successes.

Step-by-step explanation:

The first question we use the binomial distribution, while for the second we use the approximation to the normal.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution

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

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

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.

When we are approximating a binomial distribution to a normal one, we have that , .

Question a:

Here, we have .

This probability is P(X = 7). So

0.048 = 4.8% probability of exactly seven successes.

b) With 150 trials and a 39 chance of success, the probability of at least twenty-two successes.

Here we have

Mean and standard deviation:

This probability is, using continuity correction, , which is 1 subtracted by the p-value of Z when X = 21.5. So

has a p-value of 0

1 - 0 = 1

100% probability of at least twenty-two successes.

a) false; the points do not have to be in a straight line.

step-by-step explanation:

the points could be in the shape of a triangle

b is incorrect

c is incorrect because it is saying the immediately don't form one when they are capable of doing so

d is incorrect

the answer is: d) o, f, and kr.

atomic radius of bromine (br) is 114 pm.

atomic radius of oxygen (o) is 73 pm.

atomic radius of fluorine (f) is 72 pm.

atomic radius of krypron (kr) is 112 pm.

the atomic radius of a chemical element is a measure of the size of its atom.

the atomic radius varies with increasing atomic number, but usually increases because of increasing of number of electrons.

the atomic radius decreases across the periods because an increasing number of protons, because greater attraction between the protons and electrons.