Mathematics, 14.04.2020 22:14 edith47

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.)

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Answer from: SupremeNerdx

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 $\hat p$ = 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 = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = 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( $\hat p$ < 0.35)

P( $\hat p$ < 0.51) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\frac{0.35-0.40}{\sqrt{\frac{0.35(1-0.35)}{50} } }$ ) = P(Z < -0.74) = 1 - P(Z $\leq$ 0.74)

= 1 - 0.77035 = 0.22965

Now, in the z table the P(Z $\leq$ 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.

Answer from: Quest

You have 2 sides that are 2 cms and you have 6 sides that are 1/2 cm and you have 4 sides that are 1 cm. the smallest sides are 1/2 the medium sized sides are 1 and the smallest are 1/2. so to find the perimeter you have to add them all up together so your answer will be 11 cm's

Answer from: Quest

The answer to your question is 1/9

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