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slavikrds [6]
2 years ago
10

What is the 95% confidence interval of E(Y) at X = 4?

Mathematics
1 answer:
diamong [38]2 years ago
4 0

Based on the calculations, the 95% confidence interval of E(Y) is equal to 52.3% ± 3.26%.

<h3>How to construct a 95​% confidence interval?</h3>

Mathematically, a confidence interval of 95% is given by;

α = 1 - 0.95

α = 0.05.

α/2 = 0.05/2 = 0.025.

Next, we would determine the standard deviation of the mean:

Standard deviation of mean = 50/√800

Standard deviation of mean = 1.77.

From the z-table, the z-score of a 95% confidence interval is equal to 1.96.

Confidence interval (0.05, 50, 800) = 1.77 × 1.96

Confidence interval (0.05, 50, 800) = 3.46.

Mathematically, the confidence interval for a mean is given by:

Mean ± (t-critical × (standard deviation/√(sample size)))

Confidence interval = 52.3% ± 3.26%.

Read more on confidence interval here: brainly.com/question/25779324

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<u>Complete Question:</u>

A research team studied Y, the percentage of voters in favor of a candidate. The random variable Y had standard deviation o = 50%. A random sample of 800 voters was selected, and their average was y-bar(800) = 52.3%. What is the 95% confidence interval for E(Y)?

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How many terms are in the binomial expansion of (2x 3)5? 4 5 6 7
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In the binomial expansion (2x + 3)^5 , there are 6 terms.

According to the question, given that

Binomial expansion  (2x + 3)^5

Number of terms in a binomial expansion of (x + y)^n is

N = n + 1 words in total

In the binomial expansion (2x + 3)^5

n = 5

N = 5 + 1 = 6

Therefore, In Binomial expansion  (2x + 3)^5 there are 6 terms.

The algebraic expression (x + y)n can be expanded according to the binomial theorem, which represents it as a sum of terms using separate exponents of the variables x and y. Each word in a binomial expansion has a coefficient, which is a numerical value.

The formula for expanding the exponential power of a binomial expression is provided by the binomial theorem, sometimes referred to as the binomial expansion. The following is the binomial expansion of (x + y)n using the binomial theorem:

(x+y)^n = n_C_{0} * n_y_{0} + n_C_{1}  * n-1_y_{1} + n_C_{2} * n-2_ y_{2} + ... + n_C_{n-1} * 1_y_{n-1} + n_C_{n} * 0_y_{n}

To learn more about binomial theorem visit here : brainly.com/question/2165968

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