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Suppose that it is known that the heights of male Shar Pei dogs are normally distributed with a mean of 19.5 inches and a standa

emmainna [20.7K]

Answer:

0.013 = 1.3% probability that at least one is taller than 21 inches

Step-by-step explanation:

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

Binomial probability distribution

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

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Normal probability distribution

When the distribution is normal, we use 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.

Proportion of male dogs taller than 21 inches:

A mean of 19.5 inches and a standard deviation of 0.5 inches. This means that $\mu = 19.5, \sigma = 0.5$

This proportion is 1 subtracted by the pvalue of Z when X = 21.

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

$Z = \frac{21 - 19.5}{0.5}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

1 - 0.9987 = 0.0013.

In a random sample of 10 male Shar Pei dogs what is the probability that at least one is taller than 21 inches?

0.0013 of the dogs are taller than 21 inches, so $p = 0.0013$

10 dogs, so $n = 10$

Either no dog is taller than 21 inches, or at least one is. The sum of the probabilities of these events is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{10,0}.(0.0013)^{0}.(0.9987)^{10} = 0.987$

Then

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.987 = 0.013$

0.013 = 1.3% probability that at least one is taller than 21 inches

8 0

3 years ago

The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.

NARA [144]

Answer:

smaller figure: 3

larger figure: 5

or, in other words, 3/5.

Step-by-step explanation:

simplify the fraction, or 15/25.

correct me if i'm wrong. hope this helps. :)

5 0

3 years ago

Write the algebraic expression that represents the following: Forty more than a number

dedylja [7]

Answer:

x+40

Step-by-step explanation:

Let's say the the "number" is x.

"Forty more than a number" would be x+40

5 0

2 years ago

Read 2 more answers

jennifer walks 8 miles in the same time she can jog 13 miles. if her jogging speed is 8mph faster than her walking speed, how fa

Elanso [62]

Answer:

12.8mph

Step-by-step explanation:

Let 'w' represent her walking speed

->if her jogging speed is 8mph faster than her walking speed

Jogging speed= w+8

Using the time equation i.e time = dist/speed

For walking when distance is 8miles

time = dist / speed= 8/w hrs

For jogging when distance is 13miles

time = dist / speed= 13/(w+8) hrs

Equating the time

jog time = walk time

13/(w+8) = 8/w

By cross multiplying it

13w = 8w + 64

5w = 64

w=64/5

w=12.8mph

Therefore, 12.8mph is her walking speed.

5 0

3 years ago

How do you evaluate f(x)=3×3-4x+5

Mrrafil [7]

-- It'll be a lot easier if you clean up the function first.
You're not changing the function. You're just making it
easier to read and work on without mistakes.

Notice that 3x3=9 , so the function is f(x) = 9 - 4x + 5

Combine like terms, and the function is f(x) = 14 - 4x .
Much easier to work with.

-- Now, when somebody tells you to evaluate the function <em>for some number</em>,
just take their number, write it in place of 'x',and see what you've got.

Example:

f(x) = 14 - 4x

Evaluate f(x) for x = 3.

-- Write 3 in place of 'x' in the function: f(3) = 14 - 4(3)

-- 4(3) = 12 . So the function is f(3) = 14 - 12

-- Finish up the subtraction : <em> f(3) = 2</em>

You just evaluated f(x) for x=3.
Nice job !

6 0

4 years ago