Mathematics, 25.03.2020 02:13 emmie50

The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 30 liters, and standard deviation of 3.3 liters. A) What is the probability that daily production is less than 36.4 liters? Answer= (Round your answer to 4 decimal places.) B) What is the probability that daily production is more than 27.6 liters? Answer= (Round your answer to 4 decimal places.)

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Answer from: jadak2020

a) 0.9738 = 97.38% probability that daily production is less than 36.4 liters.

b) 0.7673 = 76.73% probability that daily production is more than 27.6 liters

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:

$\mu = 30, \sigma = 3.3$

A) What is the probability that daily production is less than 36.4 liters?

This is the pvalue of Z when X = 36.4. So

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

$Z = \frac{36.4 - 30}{3.3}$

Z = 1.94

Z = 1.94 has a pvalue of 0.9738.

0.9738 = 97.38% probability that daily production is less than 36.4 liters.

B) What is the probability that daily production is more than 27.6 liters?

This is 1 subtracted by the pvalue of Z when X = 27.6. So

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

$Z = \frac{27.6 - 30}{3.3}$

Z = -0.73

Z = -0.73 has a pvalue of 0.2327.

1 - 0.2327 = 0.7673

0.7673 = 76.73% probability that daily production is more than 27.6 liters

Answer from: Quest

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step-by-step explanation:

Triangle qrs is dialated according to the rule d0,2(xy)

Answer from: Quest

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

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The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 30...