Recent questions in Probability Distributions

High school probabilityAnswered question

Jadiel Bowers 2023-02-20

Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean’s weekly income is approximately normal with mean $225 and standard deviation $25. The distribution of Evan’s weekly income is approximately normal with mean $240 and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?

1) 0.67

2) 0.7000

3) 0.227

4) 0.303

5) 0.354

1) 0.67

2) 0.7000

3) 0.227

4) 0.303

5) 0.354

High school probabilityAnswered question

samkenndcnt 2023-01-24

What is the formula of ${\left(A+B\right)}^{3}$?

High school probabilityAnswered question

phumzaRdY 2022-11-27

A(n) _______ distribution has a "bell" shape.

A) normal

B) outlier

C) relative frequency

D) polygon

A) normal

B) outlier

C) relative frequency

D) polygon

High school probabilityAnswered question

Wyatt Weeks 2022-10-19

Use the Standard Normal Distribution table to find the indicated area under the standard normal curve.

Q1: Between z = 0 and z = 2.24

$A1:0=0.5000\phantom{\rule{0ex}{0ex}}2.24=0.9875\phantom{\rule{0ex}{0ex}}0.9875\u20130.5000=0.4875$

$Q2:\text{To the left of}z=1.09\phantom{\rule{0ex}{0ex}}A2:0.8621$

Q3: Between z = -1.15 and z = -0.56

$A3:-1.15=0.1251\phantom{\rule{0ex}{0ex}}-0.56=0.2877\phantom{\rule{0ex}{0ex}}0.1251-0.2877=-0.1626$

Q4: To the right of z = -1.93

$A4:1\u20130.0268=0.9732$

Section 5.2: Normal Distributions: Find Probabilities

Q5: The diameters of a wooden dowel produced by a new machine arenormally distributed with a mean of 0.55 inches and a standarddeviation of 0.01 inches. What percent of the dowels will have adiameter greater than 0.57?

$A5:z=x-\mu /\sigma \phantom{\rule{0ex}{0ex}}=0.57\u20130.55/0.01=2\phantom{\rule{0ex}{0ex}}=P(x>0.57)\phantom{\rule{0ex}{0ex}}=P(z>2)\phantom{\rule{0ex}{0ex}}=1\u2013P(z<2)\phantom{\rule{0ex}{0ex}}=1\u20130.9772\phantom{\rule{0ex}{0ex}}=0.0228$

Q6: A loan officer rates applicants for credit. Ratings arenormally distributed. The mean is 240 and the standard deviation is50. Find the probability that an applicant will have a ratinggreater than 260.

$A6:z=x-\mu /\sigma =260\u2013240/50\phantom{\rule{0ex}{0ex}}=0.4\phantom{\rule{0ex}{0ex}}=P(x>260)\phantom{\rule{0ex}{0ex}}=P(z>0.4)\phantom{\rule{0ex}{0ex}}=1\u2013P(z<0.4)\phantom{\rule{0ex}{0ex}}=1\u20130.6554\phantom{\rule{0ex}{0ex}}=0.9772$

Q1: Between z = 0 and z = 2.24

$A1:0=0.5000\phantom{\rule{0ex}{0ex}}2.24=0.9875\phantom{\rule{0ex}{0ex}}0.9875\u20130.5000=0.4875$

$Q2:\text{To the left of}z=1.09\phantom{\rule{0ex}{0ex}}A2:0.8621$

Q3: Between z = -1.15 and z = -0.56

$A3:-1.15=0.1251\phantom{\rule{0ex}{0ex}}-0.56=0.2877\phantom{\rule{0ex}{0ex}}0.1251-0.2877=-0.1626$

Q4: To the right of z = -1.93

$A4:1\u20130.0268=0.9732$

Section 5.2: Normal Distributions: Find Probabilities

Q5: The diameters of a wooden dowel produced by a new machine arenormally distributed with a mean of 0.55 inches and a standarddeviation of 0.01 inches. What percent of the dowels will have adiameter greater than 0.57?

$A5:z=x-\mu /\sigma \phantom{\rule{0ex}{0ex}}=0.57\u20130.55/0.01=2\phantom{\rule{0ex}{0ex}}=P(x>0.57)\phantom{\rule{0ex}{0ex}}=P(z>2)\phantom{\rule{0ex}{0ex}}=1\u2013P(z<2)\phantom{\rule{0ex}{0ex}}=1\u20130.9772\phantom{\rule{0ex}{0ex}}=0.0228$

Q6: A loan officer rates applicants for credit. Ratings arenormally distributed. The mean is 240 and the standard deviation is50. Find the probability that an applicant will have a ratinggreater than 260.

$A6:z=x-\mu /\sigma =260\u2013240/50\phantom{\rule{0ex}{0ex}}=0.4\phantom{\rule{0ex}{0ex}}=P(x>260)\phantom{\rule{0ex}{0ex}}=P(z>0.4)\phantom{\rule{0ex}{0ex}}=1\u2013P(z<0.4)\phantom{\rule{0ex}{0ex}}=1\u20130.6554\phantom{\rule{0ex}{0ex}}=0.9772$

Probability distributions are mathematical models that help us understand the likelihood of an event occurring. Common distributions include normal, binomial, Poisson, exponential, and Chi-squared. To understand these distributions, it is important to understand the equations behind them and how to use them to solve problems. Our math site has a comprehensive list of probability distributions with examples and equations to help you understand and solve problems. We also provide step-by-step solutions with answers and explanations to help you learn and understand the concepts better. Check out our questions to get help with probability distributions.