Research in March 2019 suggests that 40% of U. S. adults approve of way President Trump is running the country. We randomly sample 50 U. S. adults and find that 35% approve of way President Trump is running the country.
What is the probability that a random sample of 50 U. S. adults has less than 35% with this opinion? (Round standard error to 2 decimal places before calculating Z. Round Z to 2 decimal places before using the Normal Distribution Calculator.)

Probability that a random sample of 50 U.S. adults has less than 35% with this opinion is 0.22965.

Step-by-step explanation:

We are given that Research in March 2019 suggests that 40% of U.S. adults approve of way President Trump is running the country. We randomly sample 50 U.S. adults and find that 35% approve of way President Trump is running the country.

Let = sample proportion of U.S.adults politicians who approve of way President Trump is running the country.

The z-score probability distribution for sample proportion is given by;

            Z =  ~ N(0,1)

where, = sample proportion

           p = population proportion = 40%

           n = sample of U.S. adults = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that a random sample of 50 U.S. adults has less than 35% with this opinion is given by = P( < 0.35)

  P( < 0.51) = P( < ) = P(Z < -0.74) = 1 - P(Z 0.74)

                                                                = 1 - 0.77035 = 0.22965

Now, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.74 in the z table which has an area of 0.77035.

Therefore, probability that a random sample of 50 U.S. adults has less than 35% with this opinion is 0.22965.

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,