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Sagot :
Answer:
7.57
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.
The height of sunflowers is Normally distributed with mean 50 inches and standard deviation 8 inches.
This means that [tex]\mu = 50, \sigma = 8[/tex]
Percent of all sunflowers that are between 35 and 40 inches tall.
As a proportion, this is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 35. So
X = 40
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 50}{8}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a pvalue of 0.1057
X = 35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 50}{8}[/tex]
[tex]Z = -1.88[/tex]
[tex]Z = -1.88[/tex] has a pvalue of 0.03
0.1057 - 0.03 = 0.0757
As percent: 0.0757*100% = 7.57%
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