In 2017, the SAT scores in the US has a mean of 1060 and a standard deviation of 195.

If a student is randomly selected, what is the probability that his/her score is less than 900? round your answer to 3 decimal places.

If a college only consider applicants with SAT scores from the top 10% what is the cutoff score ? round your answer to the nearest whole number.

If a random sample of 100 students is selected, what is the probability that the mean score is between 1100 and 1400 round your answer to 3 decimal places

According to a​ survey, 61​% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded. When technology is​ used, use the Tech Help button for further assistance.

​(a) Find the probability that exactly 40 of the murders were cleared.

​(b) Find the probability that between 36 and 38 of the​ murders, inclusive, were cleared. ​

(c) Would it be unusual if fewer than 20 of the murders were​ cleared? Why or why​ not?

An airline sells 140 tickets for a flight. Suppose the probability that any given ticket holder actually shows up for the flight is 95%. Find the probability that

a. No one shows up for the flight.

b. Everyone shows up for the flight.

c. Exactly 130 passengers show up.

d. At most 130 passengers show up.

e. At least 130 passengers show up.

f. Less than 130 passengers show up.

g. The number of passengers showing up is between 130 and 140, including 130 and 140.

1. In a shopping mall an average of 3 out of every 5 customers use visa credit cards. A sample of 10 customers is selected.
   1. Find the probability that exactly 6 customers use visa credit card.
   2. Find the probability that less than 9 customers use visa credit card.
   3. Now assume that a sample of 50 customers are selected. Find the smallest value of n such that P(X<n) ≥ 0.9, where the random variable X represents the number of customers who uses visa credit card.

A credit union is evaluating their staffing schedule to assure they have sufficient staff for their drive-up window during the lunch hour (12:00 pm to 1:00 pm). Assume the number of people who arrive at their drive-up window in a 15-minute time period during the lunch hour has a Poisson distribution with λ = 2.6.

a. What is the probability no customers will arrive between 12:15 and 12:30?

b. What is the probability fewer than 2 people will arrive between 12:15 and 12:45?

According to a​ survey, 63​% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded. When technology is​ used, use the Tech Help button for further assistance.

​(a) Find the probability that exactly 40 of the murders were cleared. ​

(b) Find the probability that between 35 and 37 of the​ murders, inclusive, were cleared.

​(c) Would it be unusual if fewer than 18 of the murders were​ cleared? Why or why​ not?

The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. ​

(a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate​ chips? ​

(b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate​ chips? ​

(c) What proportion of bags contains more than 1225 chocolate​ chips?

​(d) What is the percentile rank of a bag that contains 1475 chocolate​ chips?

A workshop makes tables. The cutting and sanding operations are independent. Based on historical data, under normal conditions, 1% of cut wood for the tables, and 2% of sanded wood for the tables are defective. Assume that one table is randomly selected from a lot of cut and sanded tables. a. What is the probability that at least one of the operations (cutting and sanding) will be defective? b. What is the probability that in a production lot of 10 tables, none of the tables is defective? c. What is the expected number of defective tables in a production lot of 15 tables? What is the standard deviation?

At a small liberal arts college, students can register for one to six courses. In a typical fall semester, 5% of students take one class, 26% take four classes, and 15% take six classes.

a) If 77% of students take four or more classes, find the probability that a randomly selected student takes five courses. What is the probability that a randomly selected student takes three classes, if 10% take at most two classes?

b) Calculate the expected value and standard deviation for the number of classes students enroll in.

The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution:

The squad is on duty 24 hours per day, 7 days per week.

a. Simulate the emergency calls for three days (note that this will require a “running,” or cumulative, hourly clock) using the random number table.