Statistics and Probability Answers

Data from an experiment show that the standard deviation is 3.6 and the mean is 23.4.
Find the probability that the reading from the experiment is more than 32.

Question 1 [10]
In the years 2007 a total 3500 UNAM students out of a sample 6000 who applied for NSFAF
student loans were successful.
Required:
a. Point estimate of p.
b. Point estimate of the proportion standard deviation (3)
c. What is the probability that the proportion of students who passed the course
is more than 0.55 (5)

A restaurant offers a 1kg steak as part of a promotion. Assume weights of the steaks are approximately normally distributed with a standard deviation of 25 grams.
X= weights of the steaks in grams
X bar= average weights of the steaks in grams
Assume that the average weights on 5 restaurants has been investigated.

Calculate the 75th percentile of the average weight of steaks for the 5 restaurants.

If you have samples of
n 1 equals 18
n1=18 and
n 2 equals 22
n2=22​, in performing the​ pooled-variance t​ test, how many degrees of freedom do you​ have?

You order some accessories online and get an estimated delivery date of June 1–June 11. You know you will be out of town June 4th, 5th, and 6th and are a little concerned about the package arriving when you are away. Assuming the delivery date follows a discrete uniform distribution, what is the likelihood your package will be delivered while you are out of town? Round your answer to four decimal places, if necessary.

Firm A employs many analysts and tries out a quantitative skill test on several hundred applicants. Because the test is unproven, results are not used in hiring. 40% of applicants show high aptitude on the test and 12% of those hired both show high aptitude on the test and achieve good job performances. The firm’s experience shows that 30% of all analysts achieve good job performance.

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height. Round your answer to one decimal place.



Height (inches) Frequency
70 -71 1
72 -73 8
74 - 75 13
76 - 77 8
78 - 79 15
80 - 81 6
82 - 83 3

Let the sample space be S={1,2,3,4,5,6,7,8,9,10}.Suppose the outcomes are equally likely. Compute the probability of the event E={2,6,10}.

In a large hospital an average of 3 out of every 5 patients ask for water with their meal. A random sample of 10 customers is selected. Assuming a binomial distribution, find the probability that i. Exactly 6 patients ask for water with their meal ii. At most 4 patients ask for water with their meal iii. At least 3 patients ask for water with their meal iv. Find the mean of this distribution v. Find the standard deviation of this distribution.
In a mainframe computer centre, execution time of programs follows an exponential distribution. The average execution time of the programs is 5 minutes. Find the probability that the execution time of programs is: i. Less than 4 minutes ii. More than 6 minutes