3. 5 points

During a flu epidemic, 35% of the school's students have the flu. Of those with the flu, 90% have high

frutty [35]

Answer: 0.8015

Step-by-step explanation:

Let F= event that a person has flu

H= event that person has a high temperature.

As per given,

P(F) =0.35

Then P(F')= 1- 0.35= 0.65 [Total probability= 1]

P(H | F) = 0.90

P(H|F') = 0.12

By Bayes theorem, we have

$P(F|H)=\dfrac{P(F)\timesP(H|F)}{P(F)\timesP(H|F)+P(F')\timesP(H|F')}\\\\=\dfrac{0.35\times0.90}{0.35\times0.90+0.65\times0.12}\\\\=\dfrac{0.315}{0.315+0.078}\approx0.8015$

Required probability = 0.8015

8 0

3 years ago

Donna earns twice as much money per month as omar does. Omar earns $209 more than alex. Together, the three workers earn 3320 pe

Blizzard [7]

Omar makes $882.25 a month

Donna = 2x
Omar = x
Alex = x - 209

4x - 209 = 3320
4x = 3529
x = $882.25

3 0

3 years ago

Given the function f(x) = x2 and k = 2, which of the following represents a horizontal shift?

melamori03 [73]

A horizontal shift would be in the form f(x±k)

6 0

3 years ago

Read 2 more answers

Which fraction has the value that's equal to 3/4

mamaluj [8]

One of the fractions that’s equal to $\frac{3}{4}$ is $\frac{12}{16}$

Solution:

Given that , we have to find fractions which has the same value as that of the fraction $\frac{3}{4}$

Now, we know that, there are several fractions with values equal to $\frac{3}{4}$

To find them, just multiply the numerator and denominator by the same number.

$\begin{array}{l}{3 \times 2=6} \\\\ {4 \times 2=8}\end{array}$

Therefore, $\frac{6}{8}$ is equal to $\frac{3}{4}$

We can do the same with 4, to get $\frac{12}{16}$ , or any other number beyond that.

Hence, one of the fractions that’s equal to $\frac{3}{4}$ is $\frac{12}{16}$

4 0

3 years ago

There are 48 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time

Stella [2.4K]

Answer:

a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.

Step-by-step explanation:

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

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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

For the sum of n trials, the mean is $\mu*n$ and the standard deviation is $s = \sigma\sqrt{n}$

In this question:

$n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71$

These values are in minutes.

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So

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

By the Central Limit Theorem

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

$Z = \frac{250 - 240}{27.71}$

$Z = 0.36$

$Z = 0.36$ has a pvalue of 0.6406

64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?

The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.

5 0

3 years ago