What is the pattern in the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,
1 answer:
You might be interested in
Answer:
97.92% probability that the mean score of your sample is between 22 and 28
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 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the mean score of your sample is between 22 and 28
This is the pvalue of Z when X = 28 subtracted by the pvalue of Z when X = 22. So
X = 28
By the Central Limit theorem
has a pvalue of 0.9896
X = 22
has a pvalue of 0.0104
0.9896 - 0.0104 = 0.9792
97.92% probability that the mean score of your sample is between 22 and 28
Divide the total amount of keys produced by the amount of keys a piano requires to find the amount of pianos a factory made:
The factory made 6204 pianos in 12 months.
Because the question asks for the amount of pianos made for the first 3 months, we'll divide the total 12 months by the 3 months the question asks for:
Now we'll divide the total amount of pianos made in 12 months by this number to find the pianos made in 3 months:
1551 pianos were made in the first 3 months of production.
The factory made 6204 pianos in 12 months.
Because the question asks for the amount of pianos made for the first 3 months, we'll divide the total 12 months by the 3 months the question asks for:
Now we'll divide the total amount of pianos made in 12 months by this number to find the pianos made in 3 months:
1551 pianos were made in the first 3 months of production.