I need some help please and thenk you
2 answers:
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Answer:
a) 0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb
b) No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
Assume that weights of males are normally distributed with a mean of 160 lb and a standard deviation of 35 lb.
This means that
Sample of 10:
This means that
a) Find the probability that it is overloaded because they have a mean weight greater than 158 lb.
This is 1 subtracted by the pvalue of Z when X = 158. So
By the Central Limit Theorem
has a pvalue of 0.4286
1 - 0.4286 = 0.5714
0.5714 = 57.14% probability that it is overloaded because they have a mean weight greater than 158 lb.
b.) Does this elevator appear to be safe?
No, because the probability of being overloaded is considerably high(57.14%). Ideally, it should be under 5%, which would be considered an unusual event.
Answer:
a)
b)
Step-by-step explanation:
Part a
We assume that the parachutist lands at random point in the interval (x=A,y=B) we have a continuous random variable X. And the distribution of X would be uniform . And the density function would be given by:
And 0 for other case.
The operation fails, if parachutist's distance to A is more than five times as much as her distance to B.
So the point P in the interval (A,B) at which the distance to A is exactly 5 times the distance to B is given by:
And we can find the probability desired like this:
And from the cumulative distribution function of X ficen by we got:
Part b
For this case we assume that
On this case we assume that
The density function for the Gamma distribution is given by:
And on this case we can find the probability using the complement rule like this:
We can solve this problem with the following excel code:
"=1-GAMMA.DIST(1;2;1;TRUE)"
And if we do it by hand we need to do this: