Each cube in this figure s a 1/2 centimeter cube. How many cubes are in the prism? [type your answer as a number]

The distribution of the difference between two proportions has mean of the difference between these proportions and standard deviation is the square root of the sum of the variances. So

In a sample of 86 units made with gold wire, 68 met the specification

This means that:

$pX = \frac{68}{86} = 0.7907$

$sX = \sqrt{\frac{0.7907*0.2093}{86}} = 0.0439$

In a sample of 120 units made with aluminum wire, 105 met the specification.

This means that:

$pY = \frac{105}{120} = 0.875$

$sY = \sqrt{\frac{0.875*0.125}{120}} = 0.0302$

Difference:

$p = pX - pY = 0.7907 - 0.875 = -0.0843$

$s = \sqrt{sX^2 + sY^2} = \sqrt{0.0439^2+0.0302^2} = 0.0533$

Confidence interval:

$p \pm zs$

In which z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ , with $\alpha$ being 1 subtracted by the confidence level.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Lower bound of the interval:

$p - zs = -0.0843 - 1.96*0.0533 = -0.1888$

Upper bound of the interval:

$p + zs = -0.0843 + 1.96*0.0533 = 0.0202$

The 95% confidence interval for the difference is (-0.1888, 0.0202).

6 0

3 years ago

Twenty-nine percent of americans say they are confident that passenger trips to the moon will occur in their lifetime. You rando

galina1969 [7]

Answer:

The probability is 0.0014

Step-by-step explanation:

When we have two possible outcomes p, q and we repeat the experiment multiple times, we apply the Binomial distribution, in this distribution the probability of getting exactly k successes in n trials is given by

$P(X=k) = nCk(p)^k(1-p)^{n-k}$

where p represents the probability of success. nCk refers to the combinations of k elements out of n elements.

In this case, p= .29 (the probability that the person says "yes" being confident that passenger trips to the moon will occur in their lifetime.

q = .71 (The probability that the person says "no")

We sample 200 americans, therefore, we have n = 200 and we need the probability that less than 40% of the people sampled answer "yes".

The 40% of 200 is 80. So, in other words, we need less than 80 people to answer yes to the question.

P(x<80) = P(x=0) + P(x=1) + P(x=2) + .... + P(x=79) = 0.00143466294 (we can use a Binomial Distribution calculator to compute this result)

Therefore, P(x < 80) = 0.0014

8 0

4 years ago