Statistics and Probability Answers

1. Find the mean and the standard deviation of the heights of male engineering students in which the heights 66 inches and 75 inches correspond to standard scores of –0.6 and 1.1, respectively.

2. A traffic study of 1,600 vehicles that passed by a checkpoint showed that their speeds were normally distributed with a mean of 97.6 kph and a standard deviation of 10.4 kph. How many vehicles had a speed of more than 100 kph?

1. A survey conducted in Mega Manila with a sample of 350 gasoline stations found that the price charged per liter of gasoline is normally distributed with a mean of P49.50 and a standard deviation of P2.75. Using the empirical rule, determine the number of stations that charge between P46.75 and P52.25.

2. The mean grade in a Physics examination was 73 and the standard deviation was 8. Determine the following: a. The standard scores (z-value) corresponding to a grade of 86. b. The grade of the student whose standard score is –0.8.

1. What is Regression Analysis?
2. What is a Least-Squares Line?

Consider the stochastic dynamical system mt+1 = rtmt, where m0 = 1 and rt = 2 with
a 50% chance and rt = 1/2 with a 50% chance (t = 0, 1, 2,...).
(a) What is the chance that m2 = 1?
(b) What is the sample space for m3 (i.e., the set of all possible values for m3)?
(c) What is the sample space for m4?

A bottle maker believes that 12% of his bottles are defective.

If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 412 bottles would be greater than 11%? Round your answer to four decimal places.

7. Ecologists have a long advocated recycling newspaper as a way of saving trees and reducing landfills. In recent years, a number of companies have gone into the business of collecting used newspapers from households and recycling them. A financial analyst for one such company has recently calculated that the firm would make a profit if the mean weekly newspaper collection from each household exceeded 1 kg. In a study to determine the feasibility of a recycling plant, a random sample of 100 households showed that the mean and the sample standard deviation of the weekly weight of newspapers discarded for recycling are (mean =1.1kg and SD=0.35Kg). Do these data provide sufficient evidence at the 1% significance level to allow the analyst to conclude that a recycling plant would be profitable? [Define your parameter and show all 6 steps procedure] (10 marks)

Find the measures of variability of the given table. A nutritionist thinks that people with low income average have less Recommended Daily Allowance (RDA) of 800mg intakes of Calcium (standard unit of Calcium for adult). He got a sample of 40 people with income below poverty level. The results are obtained in the following frequency distribution. Intake (mg) Frequency 101-200 1 201-300 1 301-400 9 401-500 13 501-600 10 601-700 6

The Bureau of Food and Drugs (BFD) monitors the effectiveness of new drugs. Some medications cause serious side effects. One particular antihistamine drug can lead to drowsiness or adversely affect the user’s ability to operate a motor vehicle. The following is a list of the frequency of reaction and the age of the person using the medication. Find the mean, median and mode. Age of Person No. Who Experienced a Reaction 16-25 12 26-35 18 36-45 22 46-55 19 56-65 17 66-75 8 76-85 4

Given P(E) = 0.25 P(F)=0.6 and P(E u F ) = 0.7 find P(E n F)