How many times larger is the volume of a cylinder if the height is doubled?

Jumbo eggs in Australia, on average, are supposed to weigh 68g. Margot is in charge of a quality control test that involves weig

Andrej [43]

Answer:

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

Step-by-step explanation:

To solve this question, we use 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 zscore 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 pvalue, 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 weight of 67g and a sample standard deviation of 1g.

This means that $\mu = 67, \sigma = 1$

Sample of 4

This means that $n = 4, s = \frac{1}{\sqrt{4}} = 0.5$

What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?

This is the pvalue of Z when X = 68.5. So

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

By the Central Limit Theorem

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

$Z = \frac{68.5 - 67}{0.5}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

6 0

3 years ago

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Which sentence demonstrates the multiplicative identity?<br><br> 1/2+0=1/2<br> 1/2•2=1<br> 1/2•1=1/2

sammy [17]

Answer:

$\huge\boxed{\frac{1}{2} *1=\frac{1}{2}}$

Step-by-step explanation:

$From~all~of~the~above~options,option~``C"~is~correct.~$

$The~best~equation~that~demonstrates~the~multiplicative~identity~is~\frac{1}{2}*1= \frac{1}{2}$

5 0

3 years ago

2(x+9)= [ ]x + [ ] what is the answer I’m struggling in math rb please help!!

Anarel [89]

Answer:

2x+18

Step-by-step explanation:

We can start by distributing the 2 to each term in the parentheses...

2(x)+2(9)

Multiply

2x+18

7 0

2 years ago

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Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 10 right angle0,−10 in the directions

quester [9]

Solution :

Let $v_0$ be the unit vector in the direction parallel to the plane and let $F_1$ be the component of F in the direction of $v_0$ and $F_2$ be the component normal to $v_0$ .