Answer:
Step-by-step explanation:
Given
The radius of the hemisphere is
The volume of a hemisphere is given by
Insert the value
Help me with this please ASAP
1 answer:
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Question:
(c) Boris also took a logic test. His z-score on that test was +0.93 . Does this change the answer to which test Boris performed better on? Explain your answer using z-scores.
Answer:
The answers to the questions are;
(a) Based on the z score, Boris perform better on his aptitude test.
(b) Based on the z score, Callie perform better on his knowledge test .
(c) For Boris since +0.93 = >
>
Yes as Boris now performed best on the logic test.
Step-by-step explanation:
The z-score of a score is a measurement of the score withe respect to its distance from the mean as a factor of the standard deviation.
To solve the question, we note that we are required to find the z score as follows.
z score is given by
Where:
z = Standard score
x = Score
σ = Standard deviation
μ = Mean
(a) To find out which test did Boris performed better usin z score, we have
Boris scored a
57 on the knowledge test and
106 on the aptitude test
Therefore the z sore for the knowledge test is
Here
x = 57
μ = 60
σ = 4.3
Therefore
= -3/4.3 = -30/43 = -0.6977
The z sore for Boris on the aptitude test is
Here
x = 106
μ = 110
σ = 7.1
= -40/17 = -0.5634
Based on the z score, Boris perform better on the aptitude test as his z score is higher (on the number line), --0.5634, compared to the z score on the knowledge test , -0.6977
(b) For Callie we have
Callie scored a
63 on the knowledge test and
114 on the aptitude test
Therefore the z sore for the knowledge test is
Here
x = 63
μ = 60
σ = 4.3
Therefore
= 3/4.3 = 30/43 = 0.6977
The z sore for Callie on the aptitude test is
Here
x = 114
μ = 110
σ = 7.1
= 40/17 = 0.5634
Based on the z score, Callie perform better on the knowledge test as his z score is higher (on the number line), 0.6977, compared to the z score on the aptitude test , 0.5634.
(c) If = +0.93 then sinc for Boris
= -0.6977 and
= - 0.5634 then
>
>
Therefore Boris now performed best on the logic test.
Answer:
There is a 29.27% probability that the flight is overbooked. This is not an unusually low probability. So it does seem too high so that changes must be made to make it lower.
Step-by-step explanation:
For each passenger, there are only two outcomes possible. Either they show up for the flight, or they do not show up. This means that we can solve this problem using binomial distribution probability concepts.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
A probability is said to be unusually low if it is lower than 5%.
For this problem, we have that:
There are 200 reservations, so .
A passenger consists in a passenger not showing up. There is a .0995 probability that a passenger with a reservation will not show up for the flight. So .
Find the probability that when 200 reservations are accepted for United Flight 15, there are more passengers showing up than there are seats available.
X is the number of passengers that do not show up. It needs to be at least 18 for the flight not being overbooked. So we want to find , with
. We can use a binomial probability calculator, and we find that:
.
There is a 29.27% probability that the flight is overbooked. This is not an unusually low probability. So it does seem too high so that changes must be made to make it lower.