- You’re going to catch a fish in the river. You know that its size is normally distributed with mean 56 inches and standard deviation 7 inches. What is the probability that you catch a fish over 60 inches? What is the probability that you catch a fish less than 50 inches?

__SOLUTION__

We are given x is normally distributed with mean (µ) = 56 and standard deviation (∂) = 7.

- P(x> 60) To calculate this probability we shall calculate the z-value for

x= (60) then we calculate the area to the right of this value from the z-test tables.

Z-value is given by, z = (x - µ)/(∂) where x is sample statistic,µ is the population mean and ∂ is the standard deviation.

Z for x = 60, z(60) = (60-56)/7 = 0.5714 to2decimal place is 0.57

For p(x>60) we calculate from z tables the area to the right of 0.57 from z tables, thus p(x>60) = 1-0.7157= 0.2843

Therefore the probability that one catches a fish over 60inches is 0.2843

- We are given x is normally distributed with mean (µ) = 56 and standard deviation (∂) = 7.

P(x<50) to calculate this probability we shall calculate the z-value for

x= (57) then we calculate the area to the left of this value from the z-test tables.

Z-value is given by, z = (x - µ) / (∂) where x is sample statistic,µ is the population mean and ∂ is the standard deviation.

Z for x = 50, z (50) = (50-56)/7 = -6/7 = -0.8571 to 2decimal place = -0.86

For p(x<50) we calculate from z tables the area to the left of -0.86 from z tables, thus p(x<50) = 0.1949

Therefore the probability that one catches a fish over 60inches is 0.1949

- Construct a 95% confidence interval if the sample size is 30, mean is 60 and the standard deviation is 8.

__SOLUTION__

Confidence interval ( CI) = Sample Mean (x) ±( (zα * ∂)/√n) where x is sample mean,zα is the value of z for significance level given, ∂ is the standard deviation and √n is the square root of n

Thus, CI = x ± ((zα * ∂)/√n),

CI = 60 ± ((Z0.05 * 8) / √30), = 60 ± ((1.96 * 8) / √30

CI = (60 - 2.8628, 60 - 2.8628)

CI = (57.1372, 62.8628)

Therefore the 95%confidence interval is (57.1372, 62.8628)

Assignment Writing Help

- Science Assignment Help
- Math Assignment Help
- Chemistry Assignment Help
- Physics Assignment Help
- Biology Assignment Help
- Psychology Assignment Help
- History Assignment Help
- Geography Assignment Help
- English Assignment Help
- Humanities Assignment Help
- Nursing Assignment Help
- Social Science Assignment Help
- Arts and Architecture Help
- Statistics Assignment Help
- Law Assignment Help
- Computational Mathematics Assignment Help

Engineering Assignment Services

- Programming Assignment Help
- Database Help
- Data Structure Assignment Help
- Operating Systems Assignment Help
- Computer Network Assignment Help
- UML Diagram Assignment Help
- IT Assignment Help
- Game Programming Help
- Computer Science Assignment Help
- Information Systems Assignment Help
- Chemical Engineering Assignment Help
- Civil Engineering Assignment Help
- Electrical, Electronics Help
- Mechanical Engineering Assignment Help
- Petroleum Engineering Assignment Help
- Biochemical and Biotechnology Help

Do My Assignment Help

- Accounting Assignment Help
- Finance Assignment Help
- Economics Assignment Help
- Marketing Assignment Help
- Human Resources Assignment Help
- Operations Management Assignment Help
- Strategy and Planning Help
- Project Management Help
- Case Studies Writing Help
- Political science
- Referencing Help
- Assignment Help Websites
- Online Assignment Help
- Do My Assignment
- Do My Homework
- Health Informatics

Write My Essay Services

- Essay Writing Help
- Business Essay Writing Help
- Assignment Writing Services
- Plagiarism Free Essay Writing
- Essay Editing Service
- Dissertation Writing Services
- Thesis Writing Help
- Custom Writing Help
- Write My Essay
- Write My Paper
- Paper Writing Service
- Academic Writing Help
- College Essay Writing
- Cheap Essay Writing