Which value for x makes the sentence true?

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assum

Savatey [412]

Answer:

Hence the correct option is Option b that is the same for each interval.

Step-by-step explanation:

The PDF for Uniform distribution in [a,b] is given by

$f(x)=\frac{1}{b-a}~~~~~~a\leq x\leq b$

So the probability that the random variable assumes a value in [a,b] is given by

$\int_{a}^{b}f(x)dx=\int_{a}^{b}\frac{1}{b-a}dx=1$

Therefore the correct option is b. the same for each interval.

3 0

3 years ago

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6. a. What i

MrMuchimi

Answer:

0.0668, 0.0440, 92, 5000, 80

Step-by-step explanation:

a. First calculate the z-score:

z = (x - μ) / σ

z = (71 - 80) / 6

z = -1.5

Now we use a calculator or z-score table to find P(z<-1.5).

P(z<-1.5) = 0.0668

b. Again, we calculate the z-scores:

z = (x - μ) / σ

z = (89 - 80) / 6

z = 1.5

z = (x - μ) / σ

z = (92 - 80) / 6

z = 2

Using a calculator or z-score table, we want to find P(1.5<z<2). Which is equal to P(z<2) - P(z<1.5).

P(z<2) - P(z<1.5)

0.9772 - 0.9332

0.0440

c. This time we want to go backwards. We need to find the z score such that P(z>?) = 0.0250. Or P(z<?) = 1 - 0.0250 = 0.9750. According to the table, z = 1.96.

Now finding the x value that gives us that z-score:

z = (x - μ) / σ

1.96 = (x - 80) / 6

11.76 = x - 80

x = 91.76

Since scores have to be whole numbers, we round up to 92.

d. From part b, we know the z-score for this is 1.5, and that P(z<1.5) = 0.9332. That means that P(z>1.5) = 1 - 0.9332 = 0.0668.

So if 334 scores make up 6.68% of all scores, then the number of students who took the exam is:

0.0668 N = 334

N = 5000

e. For a normal distribution, the median is also the mean. 80.

5 0

4 years ago

Daniel spent 3 hours babysitting for his brother. He and the children played games for 1 3/4 hours and watched television for 1/

Nady [450]

Answer:

1 5/8 hours

Step-by-step explanation:

Time spent reading stories = total time - (time spent for games and television)

3 - (1 3/4 + 1/2) = 3 - (7/8 + 4/8) = 24/8 - 11/8 = 13/8 = 1 5/8 hours

4 0

2 years ago

When Elena throws a shot put during track and field practice, it travels an average of 26 feet with a standard deviation of 3 fe

alexgriva [62]

Answer:

15.87%, that is, approxiately 16% of of her shots will travel less than 23 feet.

Step-by-step explanation:

Problems of normally distributed samples can be 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.

In this question, we have that:

$\mu = 26, \sigma = 3$

Approximately what percentage of her shots will travel less than 23 feet?

This is the pvalue of Z when X = 23. So

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

$Z = \frac{23 - 26}{3}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587.

15.87%, that is, approxiately 16% of of her shots will travel less than 23 feet.

5 0

4 years ago

Michael sells appliances and receives a salary of $125 per week plus a 5% commission on all sales over $750. How much does he ea

Tamiku [17]

Answer: $231.5

Step-by-step explanation:
Michael earns 5% of sales as bonus when sales cross $750. In given situation, sales are more than that so he'll get 5% of the sales, so equation becomes:
Earning= Salary + 5% of sales
Earning= 125+ 5% of 2130
Earning= 125+ 2130x5/100
Earning= 125+ 106.5
Earning = $231.5

7 0

3 years ago