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pogonyaev
3 years ago
5

A surfer recorded the maximum wave height each day at the beach for 10 days. The results are shown in this dot plot.

Mathematics
1 answer:
weqwewe [10]3 years ago
5 0

Answer:

The correct option is 3. The 10 foot wave is an outlier.

Step-by-step explanation:

The height of waves for 10 days are shown in the given figure.

From the figure it is noticed that the height of wave length is 2 for 5 days, 3 for 4 days and 10 for 1 day.

If arrange the height of wave in ascending order we get

2,2,2,2,2,3,3,3,3,10

Total number of observation is 10.

Q_1=\frac{n}{4}\text{th term}

Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}

It means Q₁ is the average of second and third term.

Q_1=\frac{2+2}{2}=2

Q_3=\frac{3n}{4}\text{th term}

Q_3=\frac{3(10)}{4}\text{th term}=7.5\text{th term}

It means Q₃ is the average of seventh and eight th term.

Q_3=\frac{3+3}{2}=3

Interquartile range is the difference between Q₃ and Q₁.

I.Q.=Q_3-Q_1=3-2=1

Q_1-1.5(I.Q.)=2-1.5=0.5

Q_3+1.5(I.Q.)=3+1.5=4.5

Therefore the data which lies outsides [0.5,4.5] are outliers of the data.

Thus, the correct option is 3. The 10 foot wave is an outlier.

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

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

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

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

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
How Ro U Sovle This Problem Bc I Don't Know How?
marissa [1.9K]
You would have to transform the fractions to decimals by dividing. For the first one, if you divide 4 by 5 you get .8. To transform a decimal to percent you move the decimal place 2 times to the right or multiply by 100 (They both would give you the same thing)
3 0
3 years ago
A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 50%
IRISSAK [1]

Answer:

a) 0.9

b) Mean = 1.58

Standard Deviation = 0.89

Step-by-step explanation:

We are given the following in the question:

A marketing firm is considering making up to three new hires.

Let X be the variable describing the number of hiring in the company.

Thus, x can take values 0,1 ,2 and 3.

P(x\geq 2) = 50\%= 0.5\\P(x = 0) = 10\% = 0.1\\P(x = 3) = 18\% = 0.18

a) P(firm will make at least one hire)

P(x\geq 2) = P(x=2) + P(x=3)\\0.5 = P(x=2) + 0.18\\ P(x=2) = 0.32

Also,

P(x= 0) +P(x= 1) + P(x= 2) + P(x= 3) = 1\\ 0.1 + P(x= 1) + 0.32 + 0.18 = 1\\ P(x= 1) = 1- (0.1+0.32+0.18) = 0.4

\text{P(firm will make at least one hire)}\\= P(x\geq 1)\\=P(x=1) + P(x=2) + P(x=3)\\ = 0.4 + 0.32 + 0.18 = 0.9

b) expected value and the standard deviation of the number of hires.

E(X) = \displaystyle\sum x_iP(x_i)\\=0(0.1) + 1(0.4) + 2(0.32)+3(0.18) = 1.58

E(x^2) = \displaystyle\sum x_i^2P(x_i)\\=0(0.1) + 1(0.4) + 4(0.32) +9(0.18) = 3.3\\V(x) = E(x^2)-[E(x)]^2 = 3.3-(1.58)^2 = 0.80\\\text{Standard Deviation} = \sqrt{V(x)} = \sqrt{0.8036} = 0.89

7 0
3 years ago
Diane must choose a number between 61 and 107 that is a multiple of 4,7, and 14 . Write all the numbers that she could choose.
Gwar [14]

Answer:

84

Step-by-step explanation:

only three number are a multiple of 14

14 * 5 = 70

14 * 6 = 84

14 * 7 = 98

neither 70 nor 98 is a multiple of 4

only 84 is a multiple of 4, 7 and 14

7 0
3 years ago
Daniella put $582 in the bank. Her brother put 3 times as much money in the bank. Her sister put 1/3 as much money in the bank.
mariarad [96]

Answer:

$2522; if her sister put in 1/3 of Daniella's original money.

But if you don't combine Daniella's original money it would be $2328

Step-by-step explanation:

582 x 3= 1746.

and 1/3 of 582= 194

582+1746+194=2522

4 0
3 years ago
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