Two 5-year girls, Alyse and Jocelyn, have been training to run a 1-mile race. Alyse's 1 mile time A is approximately Normally distributed with a mean of 13.5 and standard deviation of 2.5 minutes. Jocelyn's 1-mile time J is approximately Normally distributed with a mean of 12 minutes and a standard deviation of 1.5 minutes. Assuming A and J are independent random variables, what is the probability that Alyse has a smaller time than Jocelyn in a 1 mile race on a randomly selected day?
Answer:
1.7 × 10⁻⁴
Step-by-step explanation:
The question relates to a two sample z-test for the comparison between the means of the two samples
The null hypothesis is H₀: μ₁ ≤ μ₂
The alternative hypothesis is Hₐ: μ₁ > μ₂
[tex]z=\dfrac{(\bar{x}_1-\bar{x}_2)-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Where;
[tex]\bar {x}_1[/tex] = 13.5
[tex]\bar {x}_2[/tex] = 12
σ₁ = 2.5
σ₂ = 1.5
We set our α level at 0.05
Therefore, our critical z = ± 1.96
For n₁ = n₂ = 23, we have;
[tex]z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^{2} }{23}-\dfrac{1.5^{2}}{23}}} = 3.5969[/tex]
We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96
Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983
Therefore;
The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.
Refer the below solution for better understanding.
Step-by-step explanation:
Given :
Standard Deviation, [tex]\rm \sigma_1 = 2.5\; and\;\sigma_2= 1.5[/tex]
Calculation :
The null Hypothesis is [tex]\rm H_0: \mu_1\leq\mu_2[/tex]
The alternative Hypothesis is [tex]\rm H_a: \mu_1>\mu_2[/tex]
Now,
[tex]z = \dfrac{(\bar{x_1}-\bar{x_2})-(\mu_1-\mu_2)}{\sqrt{\dfrac{\sigma_1^2}{n_1}-\dfrac{\sigma_2^2}{n_2}} }[/tex] --------------- (1)
putting the values of
[tex]\bar{x_1}=13.5,\;\bar{x_2}=12,\;\sigma_1=2.5,\;\sigma_2=1.5[/tex]
in equation (1)
[tex]z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^2}{23}-\dfrac{1.5^2}{23}} }[/tex]
z = 3.5969
We reject the null hypothesis at
[tex]\alpha =0.05[/tex]
z-value is larger than the critical z.
3.5969 > 1.96
Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day.
The probability that Alyse has a larger time than Jocelyn is 0.99983
Therefore, the probability that Alyse has a smaller time than Jocelyn is
[tex]1-0.99983 = 0.00017 = 1.7\times10^-^4[/tex]
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The amount that Ronnie earns, E, in terms of the number of hours that he works, h, is shown in
the graph below.
What is the constant of proportionality. E/h for this situation
Answer:
8
Step-by-step explanation:
The constant of proportionality bus the amount earned by Ronnie, E, all over the corresponding hours he used in working, h.
Constant of proportionality = [tex] \frac{E}{h} [/tex]
From the graph given, when h = 5, E = 40.
Therefore:
Constant of proportionality = [tex] \frac{E}{h} = \frac{40}{5} = 8 [/tex]
Neurons are brain cells. Where would a new neuron come from?
Answer:
New neurons are born not from mature nerve cells but rather develop from neural stem cells that remain in our brains throughout life. Indeed, in some brain areas, there is continual turnover of neurons - old ones die and new ones are born - and these new neurons can participate in circuits that underlie learning.
Step-by-step explanation:
What is the Reciprocal of 5/12
Answer:
12/5 just flip the numbers :D
Step-by-step explanation:
Help!!! Quiz!! I think that the answer is A and B, but I’m not sure.
13 POINT!!!
Will mark brainliest for correct answer!!!
6x2 + 5x - 4 = 0
A. x= 1/2
B. x= -3/4
C. x= 1/3
D. x= 4
E. x= -2
F. x = -1/3
Answer:
E
Step-by-step explanation:
Hope this helped ;) Have a good day! :D
Find the slope from the table:
Answer: m=-5/3
Step-by-step explanation:
What is the slope of this line?
−3
3/4
4
−3/4
Number graph ranging from negative 5 to 5 on both the x and y axis. A line passes through the point begin ordered pair 0 comma 2 end ordered pair and the point begin ordered pair 4 comma negative 1 end ordered pair
Nick and his cousin Katie are picking apples in their grandparents' orchard. Nick has filled 15 baskets with apples and is filling them at a rate of 1 basket per hour. Katie has 10 full baskets and will continue picking at 2 baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take?
Answer:
240/4 hours will be 8 baskets
Step-by-step explanation:
1. –X + Y = -22X – Y = 6
2. X + Y = 5-2X + Y = -4
Answer:
1. –X + Y = -22X – Y = 6
2. X + Y = 5-2X + Y = -4
Step-by-step explanation:
A triangular playground has angles with measure in the ratio 6:4:5.What is the measure of the smallest angle
Answer:
36 degrees
Step-by-step explanation:
PLSS ANSWER FAST
Barnaby’s grandfather is always complaining that back when he was a teenager, he used to be able to buy his girlfriend dinner for only $1.50.
a.) If that same dinner that Barnaby’s grandfather purchased for $1.50 sixty years ago now costs $25.25 , and the price has increased exponentially, write an equation that will give you the costs at different times.
b.)How much would you expect the same dinner to cost in 60 years?
An equation that will give you the costs at different times is y = [tex]1.048^{t}[/tex].
The price of the dinner in 60 years will be $425.04.
What is the equation that represents the cost of the dinner?An exponential function is usually in the form: [tex]ab^{x}[/tex].
Where:
a = initial value b = rate of growth x = number of yearsRate of increase = (cost of the meal now / cost of the meal 60 years ago)^(1 / number of years)
(25.25 / $1.50) ^(1/60) = 4.8%
y = [tex]1.048^{t}[/tex].
What will be the cost of the meal in 60 years?25.25 x 1.048^60 = $425.04
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Sady has $545, she want to buy a boyfriend he cost $1000 on Ebay how mush does she nee to buy him?
Answer:
Sady needs $455 more dollars
Step-by-step explanation:
1,000-545=455
y+2=−3(x−4)= whats the missing equation
What do the four yellow tiles in the model of the equation below represent?
1
xxx
-4
4
-4x
4x
Alan bought a desk on sale for $589. This price was 24% less than the original price. What was the original price?
Answer:
448$
Step-by-step explanation:
100-24/100×589$
76/100×$589
divide 76 by 100 and multiple with the price which is 589$
when 76 is divided=0.76
now we multiple 0.76times 589$
I will mark. so please I WANT AN A+!!!!!
Answer:
-4.5, -3 1/2, -3, -2.5, 4 1/2
Step-by-step explanation:
the higher the numbers as a negative, the smaller they are! :)
Answer:
from least to greatest
Step-by-step explanation:
1. -4.5
2.-3 1/2
3. -3
4.-2.5
5. 4 1/2
HAVE A NICE DAY HOPE U GET A A+
The angle measures of a triangle are 2y + 3 degrees, 9y – 7 degrees, and 7y + 4 degrees. Which of the following is not one of the angle measures of the triangle?
Answer:
55
Step-by-step explanation:
The measures of the angles are 23, 83, and 74 degrees. 97 degrees is not the measure one of the angle measures of the triangle option (B) is correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
The angle measures of a triangle are 2y + 3 degrees, 9y – 7 degrees, and 7y + 4 degrees.
As we know,
The sum of the interior angle of the triangle is 180 degrees
2y + 3 + 9y - 7 + 7y + 4 = 180
18y = 180
y = 10
2y + 3 = 2(10) + 3 = 23 degres
9y - 7 = 9(10) - 7 = 83 degrees
7y + 4 = 7(10) + 4 = 74 degrees
Thus, the measures of the angles are 23, 83, and 74 degrees. 97 degrees is not the measure one of the angle measures of the triangle option (B) is correct.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
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Please answer correctly !!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
round 13.045 to the nearest hundreth
Answer:
13.00
Step-by-step explanation:
What is X-y=-1 written in y=mx+b form?
Answer:
y = x + 1
Step-by-step explanation:
please an someone help me 5(−3.4k−7)+(3k+21)
Answer:
4
Step-by-step explanation:
Answer:
4.5k
Step-by-step explanation:
which TWO Points cannot be included in the function that includes (-2,6),(-1,4),(0,2),(1,0)(3,-4) and (4,6)
A).(-4,10)
B). (-1,5)
C).(2,-3)
D).(4,8)
E).(6,-9)
Answer:
B D
Step-by-step explanation:
I need help whoever answers this question will be the brainliest!!!
Answer:
7
Step-by-step explanation:
a) Estimate 0.42 x 0.064 by rounding both numbers to one significant figure.
b) Work out the exact value of 0.42 x 0.064
Answer:
A) 0.030
B) 0.026
Step-by-step explanation:
I hope this HELP! :)
Brian measures his height at 160cm to the nearest 10cm.
What is the tallest he could be?
Give the upper bound as your answer.
Answer:
170 cm is the tallest
1. What is the distance between -12 and 6 on the number
line?
is y=7x proportional
Answer: Yes. It is inversely proportional.
Step-by-step explanation:
In your question, the constant of proportionality already jump out at us which is to get y, we have to multiply x by 7. Therefore the constant of proportionality is y=7x.
negative four times the sum of a number and 3 is at least 28, translate.
Answer: [tex]-4 * (n+3) \geq 28[/tex]
Step-by-step explanation:
Negative four -> [tex]-4[/tex]
Times the sum of a number and 3 -> [tex]-4 * (n + 3)[/tex]
Is at least 28 -> [tex]-4 * (n+3) \geq 28[/tex]
5 divided by 4= 25 divided by x
wHAT IS X
Answer:
x=20
Step-by-step explanation:
so 5/4 is 1.25
so 25/x=1.25
so to find x we do 25/1.25
when we do that we get 20 so then to check if it's right we divide 25/20 and we get 1.25 so it's right
Answer:
yeet
Step-by-step explanation:
1) A ratio of 2 to 10 is the same as
*
02/14
2/12
O 1/5
2/5
Answer:1/5
Step-by-step explanation:
Two and ten divided by two equals 1 and 5 so 1/5
