Statistics and Probability Answers

Biologists gather data on a sample of fishes in a large lake. They capture, measure the length of, and release 1,000 fishes. They find that the standard deviation is 5 centimeters, and the mean is 25 centimeters. the distribution( according to histogram) is normal. approximately what percantage of fish in the lake is likely to have an length within three standard deviations of the mean?

A woman can earn Php50,000 in one year with a probability of 0.35 or lose Php15,000 over the same period with a probability of 0.65 by investing in the stocks of a certain company. Compute her expected earnings from this investment.

 In the same carnival, there is a similar game of chance. The game involves a small bag containing 30 marbles where 12 are green, 8 are yellow, and the rest are brown. You win Php 20.00 if you are able to draw a green marble, and you win Php 10.00 if you are able to draw a yellow marble. You lose Php 30.00 if you are able to draw a brown ball. If you continue to play the game, how much do you expect to win or lose in the game?

Phase 1.

1.Imagine that a wetland you are studying has a population of

5000 frogs, including bullfrogs, spring peepers, and mink frogs.

The populations of the three species are shown below

percentage of total marsh population Gender ratio

bullfrogs (30%) Males(60%) female (40%)

spring pepper (50%) Males(55%)Female(45%)

mink frog (20%) Males(52%)female (48%)

Determine the probability that the first two frogs captured are

(a) bullfrogs

(b) female bullfrogs

(c) females of any species

(d) frogs that are not spring peepers

2 (a) Design and describe a simulation that will allow you to construct

a probability distribution for the number of bullfrogs in

a sample of 30 frogs. Use it to predict the probability that the

sample will have eight or more bullfrogs.

(b) Compute the theoretical probability distribution for the

number of bullfrogs in the sample, and then compare your

simulation results with the predicted theoretical values.

(c) Design and describe a simulation that will allow you to

construct a probability distribution for the number of female

frogs of each species in a sample of 30 frogs. Use it to

predict the probability that the sample will have eight or

more females.

(d) Compute the theoretical probability distribution for the

number of females in the sample, and then compare your

simulation results with the predicted theoretical values.

In phase 2 of your study, suppose you capture 100 frogs

species number in sample

bullfrog 35

spring pepper 50

mink frog 15

Design a simulation to determine whether or not the distribution in

your sample indicates that the number of mink frogs is seriously

reduced relative to the number of spring peepers

During a 2-week period, the average number of accidents on this section of highway is 4. What is the probability of at most two accidents during a 2-week period?

There are three blue counters and six green counters in a bag. A counter is picked out of the bag, the colour noted and then replaced three times. The random variable X is the number of blue counters taken from the bag.

a) find the probability of distribution of X

b) find the probability of getting one or more blue counters

the annual salaries in a company are approximately normally distributed with a mean of r50000 and a standard deviation of r20000. what what is the probability of people who earn between r45000 and r65000?

In a job fair, 3000 aspirants applied for a job. The mean age was found to be 28 years with a standard deviation of 4years?

i)how many applicants are 33 years old and below?

ii)how many applicants are 21 years old and above?

iii)how many have aged between 24 and 30 years?

The weights of the students in a certain year level are normally distributed with a mean of 60kg and a standard deviation of 3.5kg. Find the probability that a student randomly selected from this group weighs. i) 55kg or less. ii) 68kg or more. iii) between 48kg and 53kg

Calculate the pearson correlation coefficient for the following data

X 7 2 8 4 5

Y 4 4 7 6 7