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3 years ago

A sailfish can swim u to 68 miles per hour. At this rate, how far can a sailfish swim in 1/4 hour?

Mathematics

1 answer:

Novay_Z [31]3 years ago

6 0

Answer:

C. 17 miles

Step-by-step explanation:

Divide 68 by 4 since it is a fourth of an hour

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The mean cost of a five pound bag of shrimp is 50 dollars with a variance of 64. If a sample of 43 bags of shrimp is randomly se

anyanavicka [17]

Answer:

0.4122 = 41.22% probability that the sample mean would differ from the true mean by greater than 1 dollar

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 50, \sigma = \sqrt{64} = 8, n = 43, s = \frac{8}{\sqrt{43}} = 1.22$

What is the probability that the sample mean would differ from the true mean by greater than 1 dollar?

Either it differs by 1 dollar or less, or it differs by more than one dollar. The sum of the probabilities of these events is decimal 1.

Probability it differs by 1 dollar or less:

pvalue of Z when X = 50+1 = 51 subtracted by the pvalue of Z when X = 50 - 1 = 49.

X = 51

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

By the Central Limit Theorem

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

$Z = \frac{51-50}{1.22}$

$Z = 0.82$

$Z = 0.82$ has a pvalue of 0.7939

X = 49

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

$Z = \frac{49-50}{1.22}$

$Z = -0.82$

$Z = -0.82$ has a pvalue of 0.2061

0.7939 - 0.2061 = 0.5878

Probability it differs by more than 1 dollar:

p + 0.5878 = 1

p = 0.4122

0.4122 = 41.22% probability that the sample mean would differ from the true mean by greater than 1 dollar

4 0

3 years ago

Which equation is equivalent to 4s=t+ 2?S= 1-2S=4/t+2S =t+2/4 S=t+6

Marina CMI [18]

SOLUTION:

We are to make S the subject of the formula;

$\begin{gathered} 4S\text{ = t + 2} \\ \text{Divide both sides by 4} \\ \frac{4S}{4}\text{ = }\frac{t\text{ + 2}}{4} \\ S\text{ = }\frac{t\text{ + 2}}{4} \\ \\ \end{gathered}$

The correct option is the third one.

6 0

1 year ago

zalisa [80]

Answer:

x < -7/3 or x > 5

5 0

3 years ago

Chase collects 27.34 for a fundraiser.Sydney collects 9.83 more than chase.Ally collects 4 times as much as sydney.How much mone

Vinil7 [7]

Collection of Chase = 27.34

Collection of Sydney = 9.83+27.34 = 37.17

Let ally's collection be = x

As Ally collects 4 times as much as Sydney so,

x= 4*(37.17) =148.68

Hence, Ally collects 148.68 units

8 0

3 years ago

A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag fo

ddd [48]

Answer:

Mean = 15.15

Standard deviation = 0.6062

Step-by-step explanation:

We are given a uniform distribution of quantity to be put in each bag.

Low and high filling weights:

14.1 pounds and 16.2 pounds

a = 14.1

b = 16.2

a) Mean:

$\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{14.1+16.2}{2} = 15.15$

b) Standard Deviation:

$\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\dfrac{(16.2-14.1)^2}{12}} = \sqrt{0.3675} = 0.6062$

4 0

3 years ago