A ruler costs pence.

Based on the model N(11541154,8686) describing steer weights, what are the cutoff values for a) the highest 10% of the we

yaroslaw [1]

Answer:

a) x = 1225.68

b) x = 1081.76

c) 1109.28 < x < 1198.72

Step-by-step explanation:

Given:

- Th random variable X for steer weight follows a normal distribution:

X~ N( 1154 , 86 )

Find:

a) the highest 10% of the weights?

b) the lowest 20% of the weights?

c) the middle 40% of the weights?

Solution:

a)

We will compute the corresponding Z-value for highest cut off 10%:

Z @ 0.10 = 1.28

Z = (x-u) / sd

Where,

u: Mean of the distribution.

s.d: Standard deviation of the distribution.

1.28 = (x - 1154) / 86

x = 1.28*86 + 1154

x = 1225.68

b)

We will compute the corresponding Z-value for lowest cut off 20%:

-Z @ 0.20 = -0.84

Z = (x-u) / sd

-0.84 = (x - 1154) / 86

x = -0.84*86 + 1154

x = 1081.76

c)

We will compute the corresponding Z-value for middle cut off 40%:

Z @ 0.3 = -0.52

Z @ 0.7 = 0.52

[email protected] < x < [email protected]

-.52*86 + 1154 < x < 0.52*86 + 1154

1109.28 < x < 1198.72

7 0

3 years ago

The Math 123 book includes about 230 pages (not including the back parts of the book). If you aim to complete 65% of all the pag

alina1380 [7]

Answer: 150 pages

Step-by-step explanation:

I usually just multiply the number by the percentage and it works out just fine :)

8 0

3 years ago

Y=2/3x-1 ×=-6,-3,0,3

Y_Kistochka [10]

Answer:

y=-5,-3,-1,1 are value for y

4 0

2 years ago

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words pe

VikaD [51]

Answer:

36.04% probability that at most two of them would read at less than 850 words per minute

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution

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.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$