Theresa rolled a number cube, number 1 through 6, two times

Here are Babe Ruth's home run totals for the New York Yankees during the years 1920 - 1934:54, 59, 35, 41, 46, 25, 47, 60, 54, 4

Irina-Kira [14]

Given data is 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22

Arranging it in increasing order:

22 25 34 35 41 41 46 46 46 47 49 54 54 59 60

Number of data items, n=15.

Finding Median, First Quartile, and Third Quartile

$Finding\;\;median\\M=\frac{n+1}{2}th\;\;term =\frac{15+1}{2}=8th\;\;term\;\; i.e. \;\;46$

22 25 34 35 41 41 46 46 46 47 49 54 54 59 60

Now finding First Quartile from set: 22 25 34 35 41 41 46

Q₁ = middle term i.e. 35

Now finding Third Quartile from set: 46 47 49 54 54 59 60

Q₃ = middle term i.e. 54

So we have Q₁ = 35, M = 46, and Q₃ = 54. Lower bound is 22 and Upper bound is 60.

While drawing the given data on number line and marking First quartile, Median, Third quartile on number line. We can clearly observe that option A matches with given data points.

Hence, option A i.e. Box-plot A is the correct choice.

5 0

2 years ago

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The geometric sequence a i a i a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 =8a, start subscr

frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0

2 years ago

It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impa

lana66690 [7]

Since you know that the hose will fill the whole pool in 8 minutes you know it will fill 1/8 of the pool per minute. In 5 minutes it will fill up 5/8 of the pool. This will make your equation 5/8 +5r=1. Solving for r will give you 3 parts/40 minutes

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2 years ago

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44 students completed some homework and the histogram shows information about the times taken. Work out an estimate of the inter

Vilka [71]

Answer:

q1=11

q3= 33

Step-by-step explanation:

The data set has 44 number of students. The first quartile is 25 % of the numbers in the data set . So

25 % of 44 = 25/100 * 44= 0.25 *44 = 11

So the first quartile lies at 11.

Similarly the third quartile lies at the 75 % of the numbers of the data set . So

75 % of 44 = 75/100 * 44= 0.75 *44 = 33

So the third quartile lies at 33.

5 0

2 years ago

Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .