g.o. has 3 orange picks for every two green . if there are 25 picks in all , how many picks are orange
1 answer:
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Answer:
P(X > 0.3) = 0.3897
Step-by-step explanation:
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
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
Applying the central limit theorem:
P( > 0.3)
This is 1 subtracted by the pvalue of Z when X = 0.3. So
By the Central Limit Theorem
has a pvalue of 0.6103
1 - 0.6103 = 0.3897
So
P(X > 0.3) = 0.3897