Consider the standard normal distribution with mean  = 0, and standard deviation  = 1

a. What is the probability that an outcome z is greater than 2.20? b. What is the probability that z is less than 1.1? c. What is the probability that z is between -1.03 and 0.84? d. What value of z cuts off the upper 23% of the standard normal distribution? e. What value of z cuts off the lower 18% of the standard normal distribution?

A random sample of n = 100 observations is drawn from a population with mean 10 and variance 400.

(a) Describe the shape of the sampling distribution of ¯x. Does your answer depend on the sample size? (

b) Give the mean and standard deviation of the sampling distribution of ¯x.

(c) Find the probability that ¯x is less than 8.

(d) Find the probability that ¯x is greater than 9.5.

(e) Find the probability that ¯x is between 8 and 9.5.

The records of Check$mart Bank show that the average credit card balance of its customers is $3,325 with a standard deviation of $1,500. Assume that the distribution of these credit card balances is approximately normal.

(a) What is the probability that an account balance is less than $2,500?

(b) What is the probability that an account balance is more than $5,000?

(c) What is the probability that an account balance is between $3,000 and $4,000?

(d) 99% of account balances are less than which amount?

The SAT scores for US high school students are normally distributed with a mean of 1500 and a standard deviation of 100.

1. Calculate the probability that a randomly selected student has a SAT score greater than 1650.

2. Calculate the probability that a randomly selected student has a SAT score between 1400 and 1650, inclusive.

3. If we have random sample of 100 students, find the probability that the mean scores between 1485 and 1510, inclusive.

1) Compute the probability of drawing two clubs from a standard deck of 52 cards. Round your answer to four decimal places.

1. Answer:

Compute the probability of drawing two face cards from a standard deck of 52 cards. Round your answer to four decimal places.

1. Answer:

Compute the probability of drawing two aces from a standard deck of 52 cards. Round your answer to four decimal places.

1. Answer:

The distance between flaws on a long cable is exponentially distributed with a mean of 12 m.

a) Find the probability that the distance between two flaws is greater than 15 m.

b) Find the probability that the distance between two flaws is greater than 25 m given that it is greater than 10 m.

c) Find the probability that the distance between two flaws is greater than 20 m given that it is greater than 10 m.

he commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012). a.) Find the height of this uniform distribution. b.) Find the probability of waiting between four and five minutes. c.) Find the probability of waiting between three and eight minutes. d.) Find the probability of waiting five minutes exactl

A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is 650,000​, and the standard deviation is 200,000. A random sample of 100

agents is​ selected, and the value of the properties they sold in a year is recorded.

a. What is the standard error of the sample​ mean?

b. What is the probability that the sample mean exceeds 656,000​?

c. What is the probability that the sample mean exceeds 631,000​?

d. What is the probability that the sample mean is between 634,000

and 660,000​?

Consider a thin spherical shell located between r = 0.49a₀ and 0.51a₀. For the n = 2, l = 1 state of hydrogen, find the probability for the electron to be found in a small volume element that subtends a polar angle of 0.11° and an azimuthal angle of 0.25° if the center of the volume element is located at: θ=50°, ϕ=20°.