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Answer:
0.1% probability that the average score of a random sample of 20 students exceeds 59.5.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
Normal probability distribution
Problems of normally distributed samples 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.
In this problem, we have that:
What is the probability that the average score of a random sample of 20 students exceeds 59.5?
This is 1 subtracted by the pvalue of Z when . So
has a pvalue of 0.9990.
So there is a 1-0.9990 = 0.001 = 0.1% probability that the average score of a random sample of 20 students exceeds 59.5.
This question is incomplete, here is the complete question
What is the recursive formula for this geometric sequence 2, -10, 50, -250, .... ?
The recursive formula for this geometric sequence is:
= 2;
= (-5) •
Step-by-step explanation:
To find the recursive formula for a geometric sequence:
- Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
- Find the common ratio. (The number you multiply or divide.)
- Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.
The recursive formula is:
= first term;
= r •
, where
is the first term in the sequence
is the term before the nth term
- r is the common ratio
∵ The geometric sequence is 2 , -10 , 50 , -250
∴ = 2
- To find r divide the 2nd term by the first term
∵
∴
- Substitute the values of and r in the formula above
∴ = 2;
= (-5) •
The recursive formula for this geometric sequence is:
= 2;
= (-5) •
Learn more:
You can learn more about the geometric sequence in brainly.com/question/1522572
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