The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 210.00 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answer:
a) 0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b) 0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c) The distribution of the population is normal, which means that the sample size does not need to exceed 30.
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.3 cm.
This means that [tex]\mu = 200, \sigma = 8.3[/tex]
a. Find the probability that an individual distance is greater than 210.00 cm.
This is 1 subtracted by the pvalue of Z when X = 210. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{210 - 200}{8.3}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
1 - 0.8849 = 0.1151
0.1151 = 11.51% probability that an individual distance is greater than 210.00 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 197.80 cm
Now [tex]n = 20, s = \frac{8.3}{\sqrt{20}} = 1.8559[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 197.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{197.8 - 200}{1.8559}[/tex]
[tex]Z = -1.19[/tex]
[tex]Z = -1.19[/tex] has a pvalue of 0.117
1 - 0.117 = 0.883
0.883 = 88.3% probability that the mean for 20 randomly selected distances is greater than 197.80 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
The distribution of the population is normal, which means that the sample size does not need to exceed 30.
Find the area of this figure
Mr.moss has 4 gallons of paint. He painted 8 doors. How many benches can he paint with the paint that is left
Answer:
2
Step-by-step explanation:
I did 8 divided by 4 which is 2.
I hope this helps.
What is 4^2 - (3.1 + 6.4) + 4.5 pls show ur work
If 42,800 dollars is invested at an interest rate of 5 percent per year, find the value of the investment at the
end of 5 years for the following compounding methods.
What is the
Annual $
Semiannual $
Monthly $
Daily $
Continuously $
Answer:
Annual $54,624.85
Semiannual $54,787.62
Monthly $54,927.75
Daily $54,955.35
Continuously $54,955.35
Step-by-step explanation:
If 42,800 dollars are invested at an interest rate of 5 percent per year, to find the value of the investment at the end of 5 years for the following compounding methods, the following calculations must be performed:
Annual $54,624.85
42,800 (1 + 0.05 / 1)^5x1 = X = 54,624.85
Semiannual $54,787.62
42,800 (1 + 0.05 / 2)^5x2 = X = 54,787.62
Monthly $54,927.75
42,800 (1 + 0.05 / 12)^5x12 = X = 54,927.75
Daily $54,955.35
42,800 (1 + 0.05 / 365)^5x365 = X = 54,955.35
Continuously $54,955.35
42,800 (1 + 0.05 / 365)^5x365 = X = 54,955.35
Algebra Unit 2Part 2 Test please show work
This it the test please do as fast as posible and show work. thank you and sorry
Write the equation in standard form for the circle x^2 + y^2 + 16x + 28 = 0.
Answer:
( x + 8 ) ^2+ y^2= 36
Step-by-step explanation:
find the product 6 * 1/3
Answer:
2
Step-by-step explanation:
Reduce the numbers with the greatest common factor which is 3
So.. 2
What is the perimeter of the triangle?
Answer: 3y + 5 cm
Step-by-step explanation: The perimeter of a triangle
is just the distance around the outside of the figure.
So just add up all the sides.
So we have y + y + y + 5 and we get 3y + 5.
(-1)15 =
................
Kenneth runs 12 laps around a track in 15 min. How many minutes per a lap is that?
**choose your answer from the choices on Slide 2, but you must show how you got your answer on the chart, blank drawing space below, or explain in words**
Answer: 1.25 minutes per lap
Step-by-step explanation:
Her total time divided by total laps is 15 divided by 12, which is 1.25
Answer:
Kenith runs 0.8 laps a minute
Step-by-step explanation:
Helpppppp please i need help on this question
Step-by-step explanation:
K=12 if you want explanation i will
Francine can ride 16 miles on her bicycle in 45 minutes. At this speed, how many minutes would it take Francine to ride 60 miles?
Answer:
2000 minutes on 16 miles
Answer:
168.75 minutes
Step-by-step explanation:
Francine's speed (the unit rate) is (16 miles) / (45 minutes), or 16/45 miles/min.
Recalling that distance = speed times time, we recognize that
time = distance / speed
which here is
(60 miles) / (16/45) miles/min = 168.75 minutes, or 168 min 45 sec
Please help me I’m desperateeee
Answer:
Step-by-step explanation:
First box: (0,1)
Second box: (0,-3)
Third box: (0,-4)
also (area O O O O O O
Answer:
slide A= 6
slide B= 8
perimeter= 36
Area = 80
Step-by-step explanation:
Answer:
slide A= 6
slide B= 8
perimeter= 36
Area = 80
Step-by-step explanation:
A survey found that 73% of people use streaming services, of those who stream, 28% report that they download
movies,
Find the probability that a randomly selected person uses streaming services and downloads movies,
0.20
0.28
0.38
2.61
Answer:
0.20
Step-by-step explanation:
C/2 - 3 + 6/d when c=14 d=3
Answer:
6
Step-by-step explanation:
14/2 - 3 + 6/3
Divide 14 by 2 to get 7.
7−3+6/3
Subtract 3 from 7 to get 4.
4+6/3
Divide 6 by 3 to get 2.
4+2
Add 4 and 2 to get 6.
6
5th grade math/// In the first week of a food drive, the 5th grade collected 2 3/4 bags of canned goods. The goal is to collect 2 1/2 times as many bags in the second week. How many bags is the 5th grade hoping to collect in the second week?
The number of bags that would be collected in the second week is 6 7/8 bags.
How many bags would be collected in the second week?A mixed number is a number that is made up of an integer and a proper fraction. A proper fraction is a fraction that has a numerator that is less than the denominator. An example of a mixed number is 2 3/4.
In order to determine the number of bags that would be collected in the second week, multiply 2 3/4 by 2 1/2. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Number of bags collected in the second week = 2 3/4 x 2 1/2
11/4 x 5/2 = 55/8 = 6 7/8 bags
To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498
#SPJ1
Solve the system by substitution.
2x + 3y = 32
y = x + 9
Answer:
x=1 and y=10 (1,10)
Step-by-step explanation:
2+30=32
10=1+9
simplify 5p - 3 p + p
the answer is 3p
hope it helps!
Answer: 3p
Step-by-step explanation:
5 − 3 + =
3
PLEASEEEE HELP THIS IS DUE TODAY!!!
Answer: $200
Step-by-step explanation:
On the X axis, it shows the kilograms. Since the problem asks for how much money she makes for 60 kg, go to the point on the X axis that represents 60 kg and then go up to the corresponding y or dollar value, which is 200.
A photographer has a print that is 3.5 inches wide and 2.5 inches tall. If the photographer enlarges the print so that it is 7 inches wide, how tall will it be?
5 inches
6 inches
8 inches
12 inches
Answer:
5 inches
Step-by-step explanation:
Hope I helped
39 inches is the right answer just did the test on edge
Answer:
thanks have a nice day can you please mark me brainliest im trying to rank up and i need 2 more brainlys
Step-by-step explanation:
Which equation shown below would have a solution set to the system shown below?
x+ 2y = 4
3x - y = -1
1. 6x-2y = -1
2. 3x - y = 4
3. -2x + 3y = 5
4. 4x + y = -4
please what is the answer? i need the steps too please help me
Please help I don't get this
Answer:
18n+9
Step-by-step explanation:
9(2n+1)
multiply the 9 with the numbers in the parenthesis18n+9
The original cost is $25. The item has a discount of 20% off. What is the discount amount?
Answer:20 dollars.
not sure
Step-by-step explanation:
Work out the size of angle x.
Answer:
First: 105
Second: 65
Third: 133
Fourth: 129
Fifth: 60
A meteorologist stated that 1 foot of snowfall would melt to make 2 inches of water. Based on this rule, how much water should result from 84 inches of snowfall ?
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer:
No
Step-by-step explanation:
(2, 6) is not a solution to the given system of linear equations.
y = 5x - 4 = 5*2 - 4 = 10 - 4 = 6
y = - 1/2x + 8 = - 1/2 * 2 + 8 = - 1 + 8 = 7
Since, point (2, 6) does not satisfy to equation 2.
Therefore, (2, 6) is not a solution to the given system of linear equations.
Answer:
no
Step-by-step explanation: