-15 π + 12 π - 5 π =
1 answer:
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There are 0-14 numbers inclusive, so that means there are 15 scraps of paper.
Probability of getting greater than or equal to six (6, 7, 8, 9, 10, 11, 12, 13, 14) is
(as there are 15 scraps)
so the answer is C.
Answer:
100% probability that the sample mean scores will be between 87 and 124 points
Step-by-step explanation:
To solve this question, we have 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error
In this problem, we have that:
What is the probability that the sample mean scores will be between 87 and 124 points
This is the pvalue of Z when X = 124 subtracted by the pvalue of Z when X = 87. So
X = 124
By the Central Limit Theorem
has a pvalue of 1
X = 87
has a pvalue of 0
1 - 0 = 1
100% probability that the sample mean scores will be between 87 and 124 points