Height of the Volleyball Serve
1 answer:
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Answer:
By the Central Limit Theorem, the mean is 78, the standard deviation is and the shape is approximately normal.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 78 and a standard deviation of 6
This means that
Samples of n:
This means that the standard deviation is:
What are the mean, standard deviation, and shape of the distribution of x-bar for n?
By the Central Limit Theorem, the mean is 78, the standard deviation is and the shape is approximately normal.
Answer:
31.82% probability that this day would be a winter day
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening
In this question:
Event A: Rain
Event B: Winter day
Probability of rain:
0.42 of 0.25(winter), 0.23 of 0.25(spring), 0.16 of 0.25(summer) or 0.51 of 0.25(fall).
So
Intersection:
Rain on a winter day, which is 0.42 of 0.25. So
If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
31.82% probability that this day would be a winter day