Statistics and Probability Answers

Ophthalmology Glaucoma is an eye disease that is manifested by high intraocular pressure (IOP). The distribution of IOP in the general population is approximately normal with mean =16mmHg and standard deviation 3 mmHg. a. If the normal range for IOP is considered to be between 12 and 20 mmHg, then what percentage of the general population would fall within this range? b. If the top 5% of IOP is considered to be in danger range, then what minimum value of danger range? c. What is the 85% percentile of IOP?

To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify to be accepted into the academy. Assume the test scores are normally distributed.

A pair of fair dice is tossed. Find the probability of getting​  at most a total of 10.

1.   A random sample of n =300 observations from a binomial population produced x=125. Estimate the population proportion and determine the standard error.

Question # 1

The following table shows the distribution of fortnightly wages (in hundreds of rupees) of 80 employees working at the site of a construction project at Karachi. Daily Wages 50 – 59 , 60 – 69 , 70 – 79 , 80 – 89 , 90 – 99 , 100 – 109 , 110 – 119

No # of workers 5 , 11 , 21 , 19 , 16 , 6, 2

a)The width of class interval

.b)The frequency of second class.

c)The lower limit of the fourth class.

d)The class boundaries of the third class.

e)The class mark of the fifth class

.f)The percentage of employees earning Rs. 90 or more.

g)The percentage of employees earning less than Rs. 90

1. Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. (you may extend the table or add column or row if needed)

You volunteered to be part of the medical mission in your barangay and in-charge to get weight of the children. The weights of 1,000 children have an average of 45 kilograms and a standard deviation of 5 kilograms.

a. How many children weigh 35 kg to 55 kg?

The average length of time for students to enroll has been 50 minutes. If a random sample of 12 students incurred an average enrolment time of 42 minutes with a standard deviation of 11.9 minutes under a new enrolment system, test the hypothesis that the population mean is now less than 50 using a 0.05 level of significance. Assume that the length of time of the population is normal.

The shelf life of particular dairy products is normally distributed with u of 12 days and o of 3 days .

a. About what percent of the products last between 9 and 15 days?

b. About what percent of the products last 6 days or less

c. If a delivery of dairy products weigh 320 kg. , how many kilograms is expected to last beyond 10 days

What percent of the area under the normal curve is between z=2.25 and

z=0.58