Rectangle prism measuring 3 feet and 8 feet along the base of 5 feet tall
1 answer:
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Answer:
Yes. The sample size is large enough
H0: μ=170
Ha: μ≠ 170
a) μ= 172.52
b) 10.31
c) yes, the data is distributed around both sides of the mean
d) H0: μ=170 is true
Step-by-step explanation:
a) mean= sum of all sample values/25
(170+167+174+179+179+187+179+183+179 +156+163+156+187+156+167+156+174+170+ 183+ 179+ 174+ 179+ 170+ 159+ 187)/25 = 172.52
b) standard deviation= √(∑(x-μ)²/25)
Using this formula value of standard deviation was computed to be 10.31
c) Least value is 156, difference between least and mean is 16.52
Max value is 187, difference between max and mean is 14.48
A scatter plot shows that number of values higher than mean is 14 and number of values lower than mean is 11. So we can say that data is distributed around mean
d) Null hypthesis is accepted
Test statistic= (sample mean-expected mean)/standard deviation
=(172.52-170)/10.31
= 0.024
P(Z> 0.024)= (1-0.5080)= 0.492
p-value= 2× 0.492= 0.984
Using 5% or 0.05 significance level,
test statistic is greater than significance level so null hypothesis is accepted
Answer:
The types of trees that Logan genetically engineered are fir trees <u>9 meters</u> tall and pine trees <u>12 meters</u> tall.
Step-by-step explanation:
Given:
The combined height of one fir tree and one pine tree is 21 meters.
The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.
Now, to find the height of types of trees that Logan genetically engineered.
<em>Let the height of fir tree be </em><em />
<em>And let the height of pine tree be </em><em />
So, the combined height of both the trees:
As given, the height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.
Thus,
Now, substituting the value of from equation (1):
<em /><em />
<em>Subtracting both sides by 24 we get:</em>
<em /><em />
<em>Adding both sides by </em><em> we get:</em>
<em /><em />
<em>Dividing both sides by 5 we get:</em>
<u>The height of pine trees = 12 meters.</u>
Now, substituting the value of in equation to get the height of fir trees:
<u>The height of fir trees = 9 meters.</u>
Therefore, the types of trees that Logan genetically engineered are fir trees 9 meters tall and pine trees 12 meters tall.