1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Viktor [21]
3 years ago
9

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation

of 8.3 cm8.3 cm. a. Find the probability that an individual distance is greater than 210.90210.90 cm. b. Find the probability that the mean for 1515 randomly selected distances is greater than 196.00 cm.196.00 cm. c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?
Mathematics
1 answer:
fiasKO [112]3 years ago
5 0

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

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 \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 = 197.5, \sigma = 8.3

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

Z = \frac{210.9 - 197.5}{8.3}

Z = 1.61

Z = 1.61 has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

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

Z = \frac{196 - 197.5}{2.14}

Z = -0.7

Z = -0.7 has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

You might be interested in
jada and diego are practing the piano for sn upcoming rehersal the table list the number of minutes each of them practiced in th
Margarita [4]

Answer:

jadas practice time is 168 minutes or 2 hours 48 minutes.  Diegos practice time is 235 minutes or 3 hours 55minutes hope this helps! have a nice day and good luck with your test!

Step-by-step explanation:

4 0
2 years ago
For what value of k does the equation have no solution? kx - 4 = 5x + 8
baherus [9]

Answer:

Your answer is: k = 5+12/x

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )

7 0
3 years ago
An object launched vertically from a point that is 37.5 feet above ground level with an initial velocity of 48.6 feet per second
Elis [28]

Answer: 3.675 seconds

Step-by-step explanation:

Hi, when the object hits the ground, h=0:

h=−16t^2+48.6t+37.5

0=−16t^2+48.6t+37.5

We have to apply the quadratic formula:  

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)  

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:  

x = [ -48.6 + 69] /-32 = -0.6375

Negative:  

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

Feel free to ask for more if needed or if you did not understand something.  

8 0
3 years ago
ABCD is a parallelogram. What is the measure of ∠ACD?
Igoryamba

Step-by-step explanation:

Here

5x+16+7x-3+6x+5 = 180(being sum of triangle)

or, 18x=180-18

or, x= 162/18

so, x = 9

now,

here,

<ACD = <ACB(diagonals of parallelogram bisect eachother)

or, <ACD = 7x-3

or, <ACD = 7×9-3

or, <ACD = 63-3

So, <ACD = 60°

8 0
2 years ago
Helppppppp hurry!!!!!!!!!
lys-0071 [83]
5 is your amazing answer
3 0
3 years ago
Other questions:
  • How do i find the volume of this tunnel? Use 3.14 for pi. Please answer ASAP.
    10·2 answers
  • a steel cable weighs 2450kg the cable has a uniform circular cross section of radius 0.85cm. the steel from which thecable is ma
    8·1 answer
  • Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. Ho
    13·1 answer
  • 4(2-3x)+2=38-2x <br> I need help asap
    7·2 answers
  • Which rectangular prism has a surface area of 56 square units?
    15·2 answers
  • What is the depth of the soup ( the area shaded) 20cm is the diameter?
    14·1 answer
  • LOTS OF POINTS!! WILL GIVE BRAINLIEST!! HELP!!!!!!!!!! answer the question below.
    14·2 answers
  • 2 pounds of grapes cost $8 How do they cost per pound? How many pounds of grapes do you get per dollar?
    6·1 answer
  • 50 yards of tape is
    9·1 answer
  • Factor the following Trinomial:<br> x^2-3x+1
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!