MTH410 Midterm

If A and B are events with P(A)=0.2, P(A OR B)=0.62, and P(A AND B)=0.18, find P(B).

0.6

If A and B are independent events, P(A)=0.13, and P(B)=0.61, what is P(B|A)?

0.61

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 20 minutes, what is the probability that X is less than 23 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)

0.683

On average, Andy has noticed that 7 trains pass by his house daily (24 hours) on the nearby train tracks. What is the probability that at most 4 trains will pass his house in a 8-hour time period? (Round your answer to three decimal places.)

0.912

A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.Drawing the Blue 2 is one of the outcomes in which of the following events?

B AND E O' R OR E

If the probability that a randomly chosen college student takes statistics is 0.49, then what is the probability that a randomly chosen college student does not take statistics? Give your answer as a decimal.

By the complement rule, the probability of NOT A is 1−P(A). Therefore, the probability that a randomly chosen college student does not take statistics is 1−0.49=0.51.

You have 10 businesses that you are researching. 4 businesses only have an online shop option, 2 businesses are strictly store front and 4 businesses offer both an online shop and store front option. Given Events A and B, are the two events mutually exclusive? Explain your answer. Event A: Selecting a store with a website. Event B: Selecting a store with a store front.

No, the events are not mutually exclusive because they share the common outcome, of having both a store front and a website.

Let W be the event that a randomly chosen person works for the city government. Let V be the event that a randomly chosen person will vote in the election. Place the correct event in each response box below to show: Given that the person works for the city government, the probability that a randomly chosen person will vote in the election.

P (V | W)

The amount of time it takes Isabella to wait for the bus is continuous and uniformly distributed between 5 minutes and 20 minutes. What is the probability that it takes Isabella more than 10 minutes to wait for the bus? Round your answer to three decimal places.

P(X>10)=(20−10)(1/20−5) 0.667

If A and B are independent events with P(A)=0.5 and P(B)=0.4, find P(A AND B).

Remember that for independent events, P(A AND B)=P(A)P(B) So, plugging in the values we are given, we find that P(A AND B)=(0.5)(0.4)=0.20

John averages 58 views per hour on his webpage with a standard deviation of 11 views per hour. Suppose John's views per hour on his webpage are normally distributed. Let X= the number of views per hour on his webpage. Then X∼N(58,11).

Suppose John receives 72 views per hour on his webpage on Sunday. The z-score when x=72 is 1.273. This z-score tells you that x=72 is 1.273 standard deviations to the right of the mean, which is 58

Qualitative is _______

an attribute whose value is indicated by a label

The random variable X has a uniform distribution with values between 11 and 21. What is the mean and standard deviation of X?

mean is 16; standard deviation is 5√3/3 ≈2.887

Trial best fits which of the following descriptions?

one specific execution of an experiment

A bag contains 5 RED beads, 4 BLUE beads, and 11 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?

0.8

A deck of cards contains RED cards numbered 1,2,3,4,5, BLUE cards numbered 1,2,3,4,5,6, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is GREEN?

2/13

A grain elevator measures the weight of each truck that delivers grain to their site. What is the level of measurement of the data?

ratio

At a certain company, the mentoring program and the community outreach program meet at the same time, so it is impossible for an employee to do both. If the probability that an employee participates in the mentoring program is 0.51, and the probability that an employee participates in the outreach program is 0.21, what is the probability that an employee does the mentoring program or the community outreach program?

0.72

Carlos and Devon both accepted new jobs at different companies. Carlos's starting salary is $42,000 and Devon's starting salary is $40,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers. A website that collects salary information from a sample of employees for a number of major employers reports that Carlos's company offers a mean salary of $52,000 with a standard deviation of $8,000. Devon's company offers a mean salary of $48,000 with a standard deviation of $5,000.

Carlos's starting salary is 1.25 standard deviations below his company's mean salary and Devon's starting salary is 1.6 standard deviations below his company's mean salary. -1.25 and -1.6

A healthcare industry is reviewing the number of liabilities each location has. Location A has a z-score of −1.12 and Location N has a z-score of −0.79. Determine the area under the standard normal curve that lies to the right of the z-score −1.12 and to the left of the z-score −0.79.

First, we need to find the probabilities at each of the z-scores from the Standard Normal Table. Then we will subtract one of the areas from the other to determine the portion of the area in between. From the table, we find that P(Z<−0.79)=0.2148 and P(Z<−1.12)=0.1314. We can take the area to the left of z=−1.12 and subtract it from the area to the left of z=−0.79, to find what is left in between. P(−1.12<Z<−0.79)=P(Z<−0.79)−P(Z<−1.12)=0.2148−0.1314=0.0834 So the area between the z-scores of −1.12 and −0.79 is 0.0834. So the probability that other locations have a number of liabilities between the z-scores of −1.12 and −0.79 is 0.0834.

The probability of buying a movie ticket with a popcorn coupon is 0.608. If you buy 10 movie tickets, what is the probability that 3 or more of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)

For this problem, we could calculate each individual probability P(X=3),P(X=4),...P(X=10) but that would be very labor intensive. Instead, we can calculate 1−P(X<3). Adding these values together we get that P(X<3)=0.01. Subtract the answer from 1.

Nick wants to estimate the percentage of customers that would be satisfied with the company. He surveys 150 randomly selected customers to determine whether or not they were satisfied. What is the sample?

the 150 customers surveyed