Find the probability that a randomly chosen point in the

A raffle ticket is sold for $3.50 each and the prize for winning the raffle is $250. If 100

anygoal [31]

Expected to lose. they initially paid $350 for the tickets and are up charging the price. and the winning price is $100 less.

6 0

2 years ago

(f-g)(x) with f(x)=x + 6, g(x) = x -6

sergeinik [125]

(F-g)(x)= (x-6) + 6
= x-6+6
= x

7 0

3 years ago

Which is a logical conclusion based on the given information?

Elis [28]

Answer:

D. Triangle ACD is congruent to triangle CAB by the Hypotenuse-Leg Theorem.

Step-by-step explanation:

The Hypotenuse leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. The hypotenuse is AC for both triangles so it is the same. We are given AB = CD so ACD is congruent to CAB

6 0

3 years ago

Read 2 more answers

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 144 millimeters,

kkurt [141]

Answer:

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean diameter of 144 millimeters, and a variance of 49.

This means that $\mu = 144, \sigma = \sqrt{49} = 7$

Sample of 46:

This means that $n = 46, s = \frac{7}{\sqrt{46}}$

Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?

Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.

Probability the sample mean is below 142:

p-value of Z when X = 142, so:

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

By the Central Limit Theorem

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