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
grin007 [14]
3 years ago
13

The overhead reach distances of adult females are normally distributed with a mean of 205.5 and a standard deviation of 8.6 . a.

Find the probability that an individual distance is greater than 218.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 204.00 c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?
Mathematics
1 answer:
Anastasy [175]3 years ago
3 0

Answer:

a) 0.073044

b) 0.75033

c) The normal distribution can be used in part (b), even though the sample size does not exceed 30 because initial population size is been distributed normally , therefore, the mean of the samples will be normally distributed regardless of their size(meaning whether the sample size is less than or equal to or exceeds 30, the sample means the mean of the samples will be normally distributed regardless of their size).

Step-by-step explanation:

The overhead reach distances of adult females are normally distributed with a mean of 205.5 and a standard deviation of 8.6 .

a. Find the probability that an individual distance is greater than 218.00 cm.

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 218

μ is the population mean = 205.5

σ is the population standard deviation = 8.6

For x > 218

z = 218 - 205.5/8.6

z = 1.45349

Probability value from Z-Table:

P(x<218) = 0.92696

P(x>218) = 1 - P(x<218) = 0.073044

b. Find the probability that the mean for 15 randomly selected distances is greater than 204.00

When = random number of samples is given, we solve using this z score formula

z = (x-μ)/σ/√n

where

x is the raw score = 204

μ is the population mean = 205.5

σ is the population standard deviation = 8.6

n = 15

For x > 204

Hence

z = 204 - 205.5/8.6/√15

z = -0.67552

Probability value from Z-Table:

P(x<204) = 0.24967

P(x>204) = 1 - P(x<204) = 0.75033

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

The normal distribution can be used in part (b), even though the sample size does not exceed 30 because initial population size is been distributed normally , therefore, the mean of the samples will be normally distributed regardless of their size(meaning whether the sample size is less than or equal to or exceeds 30, the sample means the mean of the samples will be normally distributed regardless of their size).

You might be interested in
What is 0.7, 0.755, 5/8 from least to greatest?
Margarita [4]
I like to start by turning all my numbers into the same form.  You can go either way but I am going to turn the decimals into fractions.  so 0.7 is the same as 7/10.

0.755 is like 755/1000 which can be reduced to 151/200  (if you don't understand the convertions let me know i will explaine more.)

Next give all the fractions a common denominator. both 8 and 10 go into 200 so we can use that.  151/200 already has a denominator of 200 so that one is set.
for 7/10  well, 10 time 20 is 200 so multiply both the numerator and the denominator by 20 so you get 140/200
the last one is 5/8  8 times 25 is 200 so multiply both numbers by 25 to get 125/200  

the fractionos we have are 125/200  151/200 and 140/200.  Now because they all have the same denominator the one with the lowest numerator is the least number and the one with the highest number is the greatest number.

125/200  140/200  151/200  now just replace the original number with the order they are placed in.
125/200 was 5/8
140/200 was 0.7 
151/200 was 0.755
so the final answer is 
5/8, 0.7, 0.755
6 0
3 years ago
Pls help me what is the equation for this graph pls get it right :)
rewona [7]

Answer: Y= 1/8x -2

Step-by-step explanation:

Y = mx+ b

Slope = y2-y1/x2-x1 = -1+2 / 8-0 = 1/8

Initial Y-Value = -2

5 0
2 years ago
Read 2 more answers
Examine the diagram, where BD is tangent to circle M at point D, and BA is secant to the same circle at points E and A.
Stella [2.4K]

Answer:

19 = x

Step-by-step explanation:

The square of the tangent segment = The product of (whole secant segment) (the outside part of the secant segment)

BD²= (BA)(BE)        

8² = (4 + x - 7) (4)             BA = BE + EB

8² = (x - 3)(4)

64 = 4x - 12

64 + 12 = 4x

76 = 4x

19 = x

3 0
2 years ago
What is the inverse of Y=-5x-7
Pepsi [2]

Answer:y = - 5x - 7

Step-by-step explanation:The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = - 5 and b = - 7, hence

y = - 5x - 7 ← equation of line

7 0
3 years ago
A number is equal to three times the smaller number also the sum of the smaller number and four is the larger number situation i
emmainna [20.7K]

Answer:

this question is missing needed information

8 0
2 years ago
Other questions:
  • The graph shows two lines, A and B. A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line
    5·1 answer
  • Convert polar equation to rectangular coordinates θ = − (9π/ 2)
    14·1 answer
  • What is the value of x in the equation 2x + 9 = 21? (4 points)
    7·1 answer
  • (due by 9)<br> n-43=5<br> Solve for n, and show your work
    12·1 answer
  • Find the value of x and show work
    15·1 answer
  • A computer is normally $2788.43 but is discounted to $1023.99. What percent of the original price does Korey pay?​
    8·2 answers
  • A train at the local fair is 6 feet long. This 1.10 scale of an actual passenger train. You want to draw a mural that includes a
    15·1 answer
  • If s =⟨6,3⟩ and t =⟨ – 5,5⟩, find the sum s + t .
    15·1 answer
  • What product is greater than 3/5
    10·2 answers
  • Which is equivalent to 80 1/4?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!