Mathematics, 15.07.2020 04:01 kenken2583

A ranch in "Smart Town" claimed that the cows they raise are smarter than the rest of the population of US cows. To prove that they announced that the average weight of their "Smart Cow" brain is 485 grams instead of the regular 458 grams. Assume that the standard deviation of Smart Cow brain weights is the same as the entire population's standard deviation=64 g. a) What is the Probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams
b) What is the probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams

Answers: 3

Show answers

Answers

Answer from: annette211pdd8v9

(a) The probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams is 0.4091.

(b) The probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams is 0.6808.

Step-by-step explanation:

We are given that the average weight of their "Smart Cow" brain is 485 grams instead of the regular 458 grams.

Assume that the standard deviation of Smart Cow brain weights is the same as the entire population's standard deviation = 64 g.

Let X = weight of the brain of a randomly selected Smart Cow

So, X ~ Normal( $\mu=485, \sigma^{2} = 64^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean weight = 485 grams

$\sigma$ = standard deviation = 64 grams

(a) The probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams is given by = P(X $\geq$ 500 grams)

P(X $\geq$ 500 g) = P( $\frac{X-\mu}{\sigma}$ $\geq$ $\frac{500-485}{64}$ ) = P(Z $\geq$ 0.23) = 1 - P(Z < 0.23)

= 1 - 0.59095 = 0.4091

The above probability is calculated by looking at the value of x = 0.23 in the z table which has an area of 0.59095.

(b) Let $\bar X$ = sample mean weight of the brain of a randomly selected Smart Cow

The z-score probability distribution for the sample meanis given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean weight = 485 grams

$\sigma$ = standard deviation = 64 grams

n = sample of cows = 36

Now, the probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams is given by = P( $\bar X$ $\geq$ 480 grams)

P( $\bar X$ $\geq$ 480 g) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{480-485}{\frac{64}{\sqrt{36} } }$ ) = P(Z $\geq$ -0.47) = P(Z < 0.47)

= 0.6808

The above probability is calculated by looking at the value of x = 0.47 in the z table which has an area of 0.6808.

Answer from: Quest

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

Answer from: Quest

where is the gragh

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 14:20

Answers; a) 135 degree’s b) 30 degree’s c) 180 or 0 degree’s d) 90 degree’s

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

Write two subtraction equations that are equivalent to 5 + 12 = 17.

Answers: 2

Answer

Mathematics, 21.06.2019 17:00

Arestaurant offers a $12 dinner special that has 5 choices for an appetizer, 12 choices for an entrée, and 4 choices for a dessert. how many different meals are available when you select an appetizer, an entrée, and a dessert? a meal can be chosen in nothing ways. (type a whole number.)

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Rob spent 25%, percent more time on his research project than he had planned. he spent an extra h hours on the project. which of the following expressions could represent the number of hours rob actually spent on the project? two answers

Answers: 3

Answer

You know the right answer?

A ranch in "Smart Town" claimed that the cows they raise are smarter than the rest of the population...

Questions