How do you do approximate probability

The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 2300 employees at its Sam's Club warehouse unit

Advocard [28]

Answer:

(a) The mean is 52 and the median is 55.

(b) The first quartile is 44 and the third quartile is 60.

(c) The value of range is 33 and the inter-quartile range is 16.

(d) The variance is 100.143 and the standard deviation is 10.01.

(e) There are no outliers in the data set.

(f) Yes

Step-by-step explanation:

The data provided is:

S = {55, 56, 44, 43, 44, 56, 60, 62, 57, 45, 36, 38, 50, 69, 65}

(a)

Compute the mean of the data as follows:

$\bar x=\frac{1}{n}\sum x\\=\frac{1}{15}[55+ 56+ 44+ 43+ 44+ 56+ 60+ 62+ 57+ 45 +36 +38 +50 +69+ 65]\\=\frac{780}{15}\\=52$

Thus, the mean is 52.

The median for odd set of values is the computed using the formula:

$Median=(\frac{n+1}{2})^{th}\ obs.$

Arrange the data set in ascending order as follows:

36, 38, 43, 44, 44, 45, 50, 55, 56, 56, 57, 60, 62, 65, 69

There are 15 values in the set.

Compute the median value as follows:

$Median=(\frac{15+1}{2})^{th}\ obs.=(\frac{16}{2})^{th}\ obs.=8^{th}\ observation$

The 8th observation is, 55.

Thus, the median is 55.

(b)

The first quartile is the middle value of the upper-half of the data set.

The upper-half of the data set is:

36, 38, 43, 44, 44, 45, 50

The middle value of the data set is 44.

Thus, the first quartile is 44.

The third quartile is the middle value of the lower-half of the data set.

The upper-half of the data set is:

56, 56, 57, 60, 62, 65, 69

The middle value of the data set is 60.

Thus, the third quartile is 60.

(c)

The range of a data set is the difference between the maximum and minimum value.

Maximum = 69

Minimum = 36

Compute the value of Range as follows:

$Range =Maximum-Minimum\\=69-36\\=33$

Thus, the value of range is 33.

The inter-quartile range is the difference between the first and third quartile value.

Compute the value of IQR as follows:

$IQR=Q_{3}-Q_{1}\\=60-44\\=16$

Thus, the inter-quartile range is 16.

(d)

Compute the variance of the data set as follows:

$s^{2}=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=\frac{1}{15-1}[(55-52)^{2}+(56-52)^{2}+...+(65-52)^{2}]\\=100.143$

Thus, the variance is 100.143.

Compute the value of standard deviation as follows:

$s=\sqrt{s^{2}}=\sqrt{100.143}=10.01$

Thus, the standard deviation is 10.01.

(e)

An outlier is a data value that is different from the remaining values.

An outlier is a value that lies below 1.5 IQR of the first quartile or above 1.5 IQR of the third quartile.

Compute the value of Q₁ - 1.5 IQR as follows:

$Q_{1}-1.5QR=44-1.5\times 16=20$

Compute the value of Q₃ + 1.5 IQR as follows:

$Q_{3}+1.5QR=60-1.5\times 16=80$

The minimum value is 36 and the maximum is 69.

None of the values is less than 20 or more than 80.

Thus, there are no outliers in the data set.

(f)

Yes, the data provided indicates that the Walmart is meeting its goal for reducing the number of hourly employees

6 0

3 years ago

Which of the following is another way to express the equation 16 = -9 + z?

babunello [35]

Answer:

It can be anything if you put in the right number

Step-by-step explanation:

6 0

3 years ago

It has been observed that a large percentage of professional hockey players have birthdays in the first part of the year. It has

vagabundo [1.1K]

Answer:

a

$\mu = 127$

b

$\sigma = 9.76$

c

$z-score = 3.18$

d

Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158 is greater than 3( Note :the probability of z-score = 3 is 97%)

e

The correct option is option 3

Step-by-step explanation:

From the question we are told that

The population proportion is p = 0.25

The sample size is n = 508

Generally the mean is mathematically represented as

$\mu = np$

=> $\mu = 508 * 0.25$

=> $\mu = 127$

Generally the standard deviation is mathematically represented as

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

=> $\sigma = \sqrt{ 508 * 0.25 (1-0.25)}$

=> $\sigma = 9.76$

Generally the z-score of 158 is mathematically represented as

$z-score = \frac{158 - 127}{9.76}$

=> $z-score = \frac{158 - 127}{9.76}$

=> $z-score = 3.18$

Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158 is greater than 3( Note :the probability of z-score = 3 is 97%)

What this means is that the almost the whole professional hockey league player are born in the first month which is unusual

7 0

3 years ago

A spinner game has a wheel with the numbers zero through 40 marked in equally spaced slots. Consider a $1 bet on a number from 1

Svetradugi [14.3K]

Answer:

Expected return for this bet = - $0.0243

Step-by-step explanation:

to find out

the expected return for this bet

solution

we know that Number of slots in the spinner is

Number of slots in the spinner = 0 + 40 = 41 slots

so

P for you winning is here = $\frac{1}{41}$

and

Winning amount is = $40

so we can say that

Expected return for this bet is = Winning amount × P (winning) - Cost of bet ...............................1

put here value we get

Expected return for this bet = $40 × $\frac{1}{41}$ - 1

Expected return for this bet = - $0.0243

6 0

3 years ago

Help me understand this problem

Kryger [21]

It ΔABC and ΔXYZ are similar, then the sides of the triangles are in proportion.

$\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{AC}{XZ}$

We have BC = 8, AC = 7, Y = 28, XZ = 49 and YZ = 56. Substitute:

$\dfrac{AB}{XY}=\dfrac{BC}{YZ}\to\dfrac{AB}{28}=\dfrac{8}{56}\qquad\text{cross multiply}\\\\56AB=(8)(28)\qquad\text{divide both sides by 56}\\\\AB=\dfrac{224}{56}\\\\\boxed{AB=4}$

6 0

4 years ago