A survey of 100 randomly selected dentists in the state of Ohio results in 78% who would recommend the use of a certain toothpaste. The population proportion is known to be p = 0.72. For samples of size 100, which of the following best interprets the mean of the sampling distribution of sample proportion of dentists in the state of Ohio who would recommend the use of a certain toothpaste?
(a) For all random samples of 100 dentists in the state of Ohio, the sample proportion will be 0.72.
b) For all random samples of 100 dentists in the state of Ohio, the sample proportion will be 0.78.
(c) The mean of all sample proportions from all random samples of 100 dentists in the state of Ohio is equal to 0.72.
d) The mean of all sample proportions from all random samples of 100 dentists in the state of Ohio is equal to 0.78.
(e) The probability that the mean of the sampling distribution of sample proportions is greater than 0.72 is 0.78.

Step-by-step explanation:

Hello!

The sample proportion represents the number of "success" observed in a sample of n repetitions of a binomial experiment.

The study variable is:

X: number of Ohio dentists that recommend the use of a certain toothpaste in a sample of 100.

The distribution of the sample proportion is:

p'≈N(p;[p(1-p)]/n)

Where p is the population proportion and n is the sample size.

So in this distribution, the mean is "p= 0.72", which means that for all samples of Ohio dentist, the mean of dentist that recommend the use of a certain toothpaste will be 72%

You can interpret it as:

c) The mean of all sample proportions from all random samples of 100 dentists in the state of Ohio is equal to 0.72.

I hope it helps.

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4