The mean weight of a fire ant worker is 3.11 mg with a standard deviation of 0.49 mg. Let us assume that the weight of any fire ant is independent from the weight of any other fire ant. A typical fire ant colony contains 240,000 fire ant workers. Suppose we look at the weight of each ant in a typical fire ant colony. Let M be the random variable representing the mean weight of all the worker ants in the colony in mg. Let T = the random variable representing the sum of the weights of all the worker ants in the colony in mg.

The mean weight of a fire ant worker is 3.11 mg with a standard deviation of 0.49 mg. Let us assume that the weight of any fire ant is independent from the weight of any other fire ant. A typical fire ant colony contains 240,000 fire ant workers. Suppose we look at the weight of each ant in a typical fire ant colony. Let M be the random variable representing the mean weight of all the worker ants in the colony in mg. Let T = the random variable representing the sum of the weights of all the worker ants in the colony in mg.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Let X distributed as a Normal random variable with a mean of 19 and a standard deviation of 4. A)…

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…

Q: When sigma is KNOWN and n is less than 30, we use t-distribution True or false?

A: We know that when the population standard deviation (sigma) is known, then we use Z-test otherwise…

Q: Assume that ? is a random variable has a gamma distribution with (alpha) = 3 and (beta) = 10. A)…

A: Here alpha = 3 , beta = 10 Mean = 3×10 = 30 Standard deviation = 10 √3 = 17.32

Q: What is the calculator command used to find the probability of a continuous Normal random variable…

A: The Normal distribution is a continuous probability distribution that is symmetrical on both sides…

Q: Suppose that the systolic blood pressure of healthy adults is normally distributed with mean u mmHg…

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Q: Show that the standard deviation of z-scores equals 1

A: z score is given by, z score = x-μσ Where, x: Raw score μ: Population mean. σ: Population standard…

Q: Assume that women's heights are normally distributed with a mean given by μ=63.2 inches and a…

A: GivenMean(μ)=63.2standard deviation(σ)=2.5

Q: Let X be a random variable that represents the level of glucose in the blood (milligrams per…

Q: If the temperature does drop to 30°F, what is the expected number of citrus trees showing damage in…

A: Let X be the random variable the number of citrus trees showing damage in orchards.Given that,No. of…

Q: Suppose that X is a normally distributed with a mean 36 and standard deviation is 8 find the given…

A: normal distribution μ = 36σ = 8 P(x<35) = ?

Q: Assume the random variablex is normally distrubited with mean u=85 and the standard deviation o=5.…

A: Population mean μ =85 Population standard deviation =5

Q: X is a normally distributed random variable with a mean of 20 and a standard deviation of 4.75. The…

Q: The average time required to complete an accounting test has been determined to be 55 minutes with a…

A: We assume the data is normally distributed.

Q: Assume the random variable x is normally distributed with mean u=80 and standard deviation =5. Find…

A: Given that: X is normal Distributed with mean µ = 80.0 and standard deviation σ = 5.0 now will using…

Q: et X be a random variable that represents the level of glucose in the blood (milligrams per…

Q: 11. B(n=12,p=1/4). a. Find B(3); b. expected value c. standard deviation

A: Given data X~B(n=12,p=1/4) binomial distribution P(x=X) = nCxpxqn-x

Q: takes only inly not Normal. It is also highly skewed to the right, with a reported median of 200…

A: Given: μ = 338 σ = 380 n = 80

Q: The percent of fat calories that a person consumes each day is normally distributed with a mean of…

A: Solution

Q: Assume the random variable x is normally distributed with mean equals=84 and standard deviation…

A: z-score:A z-score is a standard score that describes the number of standard deviation away from its…

Q: ssume that the random variable X is normally distributed, with mean r=60 and standard deviation…

A: The z-score corresponding to x =80 will be:

Q: Assume the random variable X is normally distributed with a mean of 50 and a standard deviation of…

Q: The distribution of SAT scores is normal with a mean of µ = 500 and a standard deviation of σ = 100.…

A: Obtain the SAT score separates the top 25% of the distribution from the rest. The SAT score…

Q: Suppose that the probability is 0.2 that any given citrus tree will show measurable damage when the…

Q: (a) What is the probability that next year the total precipitation for New York State is more than…

A: (a) The random variable X is defined as the annual precipitation amount which follows normal…

Q: The weight of a tub of ice-cream from a certain brand is normally distributed with mean of 250g and…

Q: Suppose that the probability is 0.3 that any given citrus tree will show measurable damage when the…

A: Suppose that the probability is 0.3 that any given citrus tree will show measurable damage when the…

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100and a standard…

A: From the provided information, Mean (µ) = 100 Standard deviation (σ) = 20 Let X be a random variable…

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

h) What is the approximate probability that T is within 2 standard deviations of its expected value?

The mean weight of a fire ant worker is 3.11 mg with a standard deviation of 0.49 mg. Let us assume that the weight of any fire ant is
independent from the weight of any other fire ant. A typical fire ant colony contains 240,000 fire ant workers. Suppose we look at the
weight of each ant in a typical fire ant colony. Let M be the random variable representing the mean weight of all the worker ants in the
colony in mg. Let T = the random variable representing the sum of the weights of all the worker ants in the colony in mg.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The distribution of life spans is approximately normal and u=40, how large a sample is required in order that the probability of committing a type II error be 0.1 when the true mean is 35.9 months? Assume that o = 5.8 months.
Consider a random variable X that follows a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5. Calculate the probability that X is less than 40.
Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. X 0 1 2 3 4 5 P(x) 0.05 0.25 0.30 0.25 0.10 0.05 Send data to Excel
If a random member (x) is selected from a normal distribution having a mean of 80 and standard deviation of 5, what is the probability that the value of x lies between 78 and 83? Show your formula etc along with your answer.
The mean weight of all Goliath grouper caught on the Treasure coast is 367 pounds, with a standard deviation of 33 pounds. Suppose a random sample of 32 Goliath Grouper from the Treasure Coast are caught and weighed. Determine the probability that the average weight of the sample of 32 Goliath Grouper is within 7 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places , if necessary .
The grade point average for ALL juniors at a large college has a standard deviation of 0.50. A random sample of 20 students is to be used to estimate the population mean grade point average. What condition do you need to verify prior to computing the probability of obtaining a sample mean within plus or minus 0.2 of the population mean?
what is the probability in simple random sample of 50 ten gram portions of the food items result in a mean of at least 4.9 insects portions. (x-bar is 4, mean of standard deviation is 0.283.sigma is 10. original mean is 4.)