Simplify 5/4+4/1(3/4-1/2)^2
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= 33 degrees
A=33°
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW, ALSO CHECK THE ATTACHMENT FOR THE DIAGRAM
Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of S to the nearest whole degree? 19° 26° 30° 33°
EXPLANATION
Accordingto the law of cosines in
trigonometry, which gives the relationship between the lengths of the sides of a triangle to the cosine of one of its angles.
From the diagram at the attachment, the sides of the triangle are:a=10 ,b=17 ,c=18
The law can is described using the formula below;
a² = b²+ c² – 2*b*c*cos(A)
To get the angle cos(A), we make cos(A) subject of formula
cos(A)=[b²+c²-a²]/[2*b*c]
Then inserting the figures
cos (A)=[17²+18²-10²]/[2*17*18]
cos (A)=0.8382
Then find the inverse of cos(A)
A=arc cos (0.8382)
A=33.05°
A=33°( approximately)
