Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a? girl, but assume that the method has no? effect, so the probability of a girl is 0.5. Assume that the groups consist of 19 couples.
a. Find the mean and the standard deviation for the numbers of girls in groups of 19 births.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

Question

10-07-2020
Mathematics

contestada

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a? girl, but assume that the method has no? effect, so the probability of a girl is 0.5. Assume that the groups consist of 19 couples.
a. Find the mean and the standard deviation for the numbers of girls in groups of 19 births.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.

Respuesta :

Otras preguntas

Write the standard form of the line that passes through (-1,-3) and (2,1)

BRAINLIESTT What is an author's claim? EXPLAIN YOUR ANSWER A) an author's primary reason for writing a textB) a belief that is easily proved to be correct C) an

Simplify the expression. Use the varbiables, numbers, and symbols that are shown. Drag them to the appropriate box in the polynomial. Use standard polynomial fo

Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b. A.) −3.094 B.) −2.909 C.) 4.916 D.) 5.091

Define Viscosity. What are the main differences between viscous and inviscid flows?

How did Belgian imperialism affect the indigenous people living in the Congo Free State?

Which of the following is an organic compound? a. carbon monoxide (CO) b. sodium chloride (NaCl) c. sulfur oxide (SO) d. water (H2O)

Find the missing segment in the image below.

a percentage question, answer if you know, please. :)

A goal taking which of these lengths of time to achieve is most likely to be a long-term goal? A. 10 minutes B. 10 hours C. 10 years D. 10 days 2b2t

mtosi17 mtosi17 · Answer 1 · 2020-07-14T03:46:30+02:00

Answer:

a. Mean: 9.5.

Standard deviation: 2.18.

b. The critical value for signficantly low girl births is 5.14.

The critical value for signficantly high girl births is 13.86.

Step-by-step explanation:

a) If we take a sample of 19 births, all with individual probability of 0.5, we have a random binomial variable with n=19 and p=0.5.

This random variable will have mean and standard deviation calculated as:

[tex]\mu=n\cdot p=19\cdot0.5=9.5\\\\\sigma=\sqrt{np(1-p)}=\sqrt{19\cdot0.5\cdpot0.5}=\sqrt{4.75}=2.18[/tex]

b) Range rule of thumb: The standard deviation is approximately a quarter of the range, difference between the maximum and minimum value.

The range rule of thumb tells us that the expected minimum and maximum value are 2 standards deviation below or above, respectively, from the mean.

Then, the extreme expected values are:

[tex]Min=\mu-2\sigma=9.5-2\cdot2.18=9.5-4.36=5.14\\\\Max=\mu+2\sigma=9.5+2\cdot2.18=9.5+4.36=13.86[/tex]

The critical value for signficantly low girl births is 5.14.

The critical value for signficantly high girl births is 13.86.

MrRoyal MrRoyal · Answer 2 · 2021-11-16T15:12:52+01:00

The likelihood of having a girl child is its probability

The mean and the standard deviation are 9.5 and 2.18, respectively.
The values separating the significantly low and high results are 5.14 and 13.86, respectively.

The given parameters are:

[tex]\mathbf{n = 19}[/tex] --- sample size

[tex]\mathbf{p = 0.5}[/tex] --- the probability of a girl child

(a) Mean and standard deviation

The mean is calculated as:

[tex]\mathbf{Mean = np}[/tex]

So, we have:

[tex]\mathbf{\bar x= 19 \times 0.5}[/tex]

[tex]\mathbf{\bar x = 9.5}[/tex]

The standard deviation is:

[tex]\mathbf{SD = \sqrt{np(1 - p)}}[/tex]

So, we have:

[tex]\mathbf{\sigma= \sqrt{19 \times 0.5 \times (1 - 0.5)}}[/tex]

[tex]\mathbf{\sigma= \sqrt{4.75}}[/tex]

[tex]\mathbf{\sigma= 2.18}[/tex]

Hence, the mean and the standard deviation are 9.5 and 2.18, respectively.

(b) The values separating the significantly low and high results

Using the range rule of thumb, we have:

[tex]\mathbf{Low = \bar x - 2\sigma}[/tex]

[tex]\mathbf{High = \bar x + 2\sigma}[/tex]

So, we have:

[tex]\mathbf{Low= 9.5 - 2 \times 2.18 = 5.14}[/tex]

[tex]\mathbf{High= 9.5 + 2 \times 2.18 = 13.86}[/tex]

Hence, the values separating the significantly low and high results are 5.14 and 13.86, respectively.