To celebrate their 30th birthdays, brothers Mario and Luigi of the Nintendo Mario video game franchise wish to study the distrib
1 answer:
Answer:
Step-by-step explanation:
Hello!
a. The variable X: height of a Goomba. This variable has a normal distribution with mean μ= 12 inches and a standard deviation δ= 6 inches.
You need to calculate the probability that one randomly chosen Goomba has a height between 13 and 15, symbolically:
P(13≤X≤15)
Since the probability tables for the standard normal show cumulative values, you can rewrite this interval as the accumulated probability until 15 minus the accumulated probability until 13. Then or before, you can standardize the values of the variable to obtain values of Z:
P(X≤15) - P(X≤13)
P(Z≤(15-12)/6) - P(Z≤(13-12)/6)
P(Z≤0.33) - P(Z≤0.17)= 0.62930 - 0.56749= 0.06181
b. Now the study variable is Y: height of a Koopa Troopa. This variable has also a normal distribution with mean μ= 15 inches and a standard deviation δ=3 inches.
The question asks for the probability of a Koopa Troopa that is taller than 75% of Goombas.
First step:
You have to reach the value of the height of a randomly selected Koopa Troopa that is taller than 75% of the Goombas.
This means that first, you have to work under X "height of a Goompa"
And you have to look for the value of X that leaves below 0.75 of the population, symbolically:
P(X ≤ b)= 0.75
Step 2:
You have to look in the standard normal distribution for the value of Z that has below it 0.75:
Next is to reverse the standardization and clear the value of "b"
Z= (b - μ)/δ
b= (Z*δ)+μ
b= (0.674*6)+12
b= 16.044 inches
Step 3:
After learning which is the height that corresponds to a Koopa Troopa higher than 75% of the Goombas population, you have to calculate the probability of randomly selecting said Koopa:
P(Y≤16.044)
This time you'll use the mean and standard deviation of the height of the Koopa's to calculate the probability:
P(Z≤(16.044-15)/3)
P(Z≤0.348)= 0.636
The probability of randomly selecting a Koopa Troopa higher than 75% of the Goomba population is 63.6%
I hope it helps!
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The question is missing the image given to go along with it, corresponding to the map being created. The image is attached to this answer.
The side angle side (SAS) similarity theorem states that two triangles with congruent angles and sides with identical ratios then the two triangles are similar. We have various points on the map, Home (H), Park (P), Friends house (F) and Grocery store (G).
In this example, we know the angle at the point Home on the map, is shared between the two triangles. If these two triangles are similar, then the ratio of the distances HF/HG = HP/HB. We know all of these values except for the HB which is the distance from home to the bus stop. But if these triangles are similar, we can solve for that distance.
15/9 = 10/HB
HB = 90/15
HB = 6 blocks.
To determine if the triangles are similar we need to know the distance from home to the bus stop, and if these are indeed similar, that distance must be 6 blocks.
The side angle side (SAS) similarity theorem states that two triangles with congruent angles and sides with identical ratios then the two triangles are similar. We have various points on the map, Home (H), Park (P), Friends house (F) and Grocery store (G).
In this example, we know the angle at the point Home on the map, is shared between the two triangles. If these two triangles are similar, then the ratio of the distances HF/HG = HP/HB. We know all of these values except for the HB which is the distance from home to the bus stop. But if these triangles are similar, we can solve for that distance.
15/9 = 10/HB
HB = 90/15
HB = 6 blocks.
To determine if the triangles are similar we need to know the distance from home to the bus stop, and if these are indeed similar, that distance must be 6 blocks.