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marta [7]
3 years ago
13

For the wheat-yield distribution of Exercise 4.3.5, find

Mathematics
1 answer:
Setler79 [48]3 years ago
6 0

Answer:

a) 90.695 lb

b) 85.305 lb

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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.

In this problem, we have that:

\mu = 88, \sigma = 7

(a) The 65th percentile

X when Z has a pvalue of 0.65. So X when Z = 0.385.

Z = \frac{X - \mu}{\sigma}

0.385 = \frac{X - 88}{7}

X - 88 = 7*0.385

X = 90.695

(b) The 35th percentile

X when Z has a pvalue of 0.35. So X when Z = -0.385.

Z = \frac{X - \mu}{\sigma}

-0.385 = \frac{X - 88}{7}

X - 88 = 7*(-0.385)

X = 85.305

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