Suppose you pick and replace marbles from a bag, one after another. If the bag contains 3 red marbles, 3 white marbles, and 6 bl

WHO IS GOOD AT MATH!!!!! Solve this problem. 326-9²+32= ?

lesya [120]

The answer is 277......

6 0

3 years ago

A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength

irinina [24]

Answer:

Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.

Step-by-step explanation:

We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.

Let $\bar X$ = sample mean comprehensive strength

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

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean comprehensive strength = 5500 psi

$\sigma$ = standard deviation = 100 psi

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.

Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P( $\bar X$ > 4985 psi)

P( $\bar X$ > 4985 psi) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{4985-5500}{\frac{100}{\sqrt{9} } }$ ) = P(Z > -15.45) = P(Z < 15.45)

= 0.99999

Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.

4 0

3 years ago

A sample size 25 is picked up at random from a population which is normally

Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 100 and variance of 36.

This means that $\mu = 100, \sigma = \sqrt{36} = 6$

Sample of 25:

This means that $n = 25, s = \frac{6}{\sqrt{25}} = 1.2$

(a) P(X<99)

This is the pvalue of Z when X = 99. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{99 - 100}{1.2}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

$Z = \frac{X - \mu}{s}$

$Z = \frac{100 - 100}{1.2}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

X = 98

$Z = \frac{X - \mu}{s}$

$Z = \frac{98 - 100}{1.2}$

$Z = -1.67$

$Z = -1.67$ has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0

2 years ago

I need help with this！And also can they play 6 levels during their free trial?

djverab [1.8K]

Answer: B and they can play 6 levels

Step-by-step explanation: first solve the mixed fractions

Then solve the factions

7 0

2 years ago

1) Simplify into Standard Form. 2(x – 3)^2 – 1 help !

loris [4]

2x^2 - 12x + 17

you just simplify it by doing the square number to the bracket and then multiply everything in the bracket by the number outside the bracket (this example 2)

6 0

2 years ago