The acceptable level for insect filth in a certain food item is 55 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 6060 ten-gram portions of the food item is obtained and results in a sample mean of x overbarxequals=5.35.3 insect fragments per ten-gram portion. Complete parts (a) through (c) below. Part 1 (a) Why is the sampling distribution of x̄ approximately normal? A. The sampling distribution of x̄ is approximately normal because the sample size is large enough. Part 2 (b) What is the mean and standard deviation of the sampling distribution of x̄ assuming μ = 5 and σ = √5? μₓ̄ = 5 (Round to three decimal places as needed.) Part 3 σₓ̄ = 0.645 (Round to three decimal places as needed.) Part 4 (c) What is the probability a simple random sample of 60 ten-gram portions of the food item results in a mean of at least 5.3 insect fragments? P(x̄ ≥ 5.3) = (You need to calculate this probability)
The acceptable level for insect filth in a certain food item is 55 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 6060 ten-gram portions of the food item is obtained and results in a sample mean of x overbarxequals=5.35.3 insect fragments per ten-gram portion. Complete parts (a) through (c) below. Part 1 (a) Why is the sampling distribution of x̄ approximately normal? A. The sampling distribution of x̄ is approximately normal because the sample size is large enough. Part 2 (b) What is the mean and standard deviation of the sampling distribution of x̄ assuming μ = 5 and σ = √5? μₓ̄ = 5 (Round to three decimal places as needed.) Part 3 σₓ̄ = 0.645 (Round to three decimal places as needed.) Part 4 (c) What is the probability a simple random sample of 60 ten-gram portions of the food item results in a mean of at least 5.3 insect fragments? P(x̄ ≥ 5.3) = (You need to calculate this probability)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
Related questions
Question
The acceptable level for insect filth in a certain food item is
mean of
55
insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of
6060
ten-gram portions of the food item is obtained and results in a sample x overbarxequals=5.35.3
insect fragments per ten-gram portion. Complete parts (a) through (c) below.Part 1 (a) Why is the sampling distribution of x̄ approximately normal?
A. The sampling distribution of x̄ is approximately normal because the
Part 2 (b) What is the mean and standard deviation of the sampling distribution of x̄ assuming μ = 5 and σ = √5?
μₓ̄ = 5 (Round to three decimal places as needed.)
Part 3 σₓ̄ = 0.645 (Round to three decimal places as needed.)
Part 4 (c) What is the probability a simple random sample of 60 ten-gram portions of the food item results in a mean of at least 5.3 insect fragments?
P(x̄ ≥ 5.3) = (You need to calculate this probability)
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
