Answer:
or
Step-by-step explanation:
Add 21 on both sides.
a=4
b=-16
c=-5
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Jennifer has been saving for college for 57 months. The first month, she saved $11.
2 answers:
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The jar has 6+5=11 marbles.
We have to find the probability of the following event:
1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red
2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)
The probability of the first event is:
The probability of the second event is:
The probability of the both events to happen is:
Answer:
15.87% probability that a random sample of 16 people will exceed the weight limit
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 normally distributed samples are 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.
For sums, the theorem can be applied, with mean and standard deviation
In this problem, we have that:
If a random sample of 16 persons from the campus is to be taken, what is the chance that a random sample of 16 people will exceed the weight limit
This is 1 subtracted by the pvalue of Z when X = 2508. So
By the Central Limit Theorem
has a pvalue of 0.8413
1 - 0.8413 = 0.1587
15.87% probability that a random sample of 16 people will exceed the weight limit