On average, a squirrel lives to be 6.5 years old. The lifespan of a squirrel may
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Answer:
a) P(7.99 ≤ X ≤ 8.01) = 0.8164
b) P(X ≥ 8.01) = 0.0475.
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
, the sample means with size n can be approximated to a normal distribution with mean
In this problem, we have that:
(a) Calculate P(7.99 ≤ X ≤ 8.01) when n = 16.
n = 16, so
This probability is the pvalue of Z when X = 8.01 subtracted by the pvalue of Z when X = 7.99. So
X = 8.01
Applying the Central Limit Theorem
has a pvalue of 0.9082
X = 7.99
has a pvalue of 0.0918
0.9082 - 0.0918 = 0.8164
P(7.99 ≤ X ≤ 8.01) = 0.8164
(b) How likely is it that the sample mean diameter exceeds 8.01 when n = 25? P(X ≥ 8.01) =
n = 25, so
This is 1 subtracted by the pvalue of Z when X = 8.01. So
has a pvalue of 0.9525
1 - 0.9525 = 0.0475
P(X ≥ 8.01) = 0.0475.
Answer:
<h2>d = 8</h2><h2>g = 2</h2>Step-by-step explanation:
8d + 4 = 5d + 28
Group like terms
That's
8d - 5d = 28 - 4
3d = 24
Divide both sides by 3
d = 8
Cross multiply
we have
7(7g + 8) = 38.5(4)
49g + 56 = 154
49g = 154 - 56
49g = 98
Divide both sides by 49
g = 2
Hope this helps you