# Homework assignment

*label*Mathematics

*timer*Asked: Jun 30th, 2018

*account_balance_wallet*$25

**Question description**

Hi, I hope all is well. Please look at the 2 files attached and do them. Let me know if you need anything. Thanks again for helping me. I will also need your help with other assignments. Thanks again.

## Tutor Answer

Attached.

Homework 3 (50 pts) Due 6/29

1. In an agricultural experiment, a large field of wheat was divided into many plots

(each plot being 7 x 100 ft) and the yield of grain was measured for each plot. These plot yields

approximately followed a normal distribution with mean 70 lbs. and SD 8 lbs.

a) Let Y represent the yield rate of a randomly selected plot. Find the percentage of plots

with a yield rate greater than 80 lbs.

80 β π₯Μ

π(π > 80) = π (π§ >

) = π(π§ > 1.25) = 1 β 0.8944 = 0.1056

π

10.56%

b) Let M1represent the mean yield rate of 5 plots chosen at random from the

field.According to CLT, what is the mean and standard deviation of M1? And find the

probability of getting the average yield rate greater than 80 lbs.

π

π₯Μ
= 70 π2 =

= 3.58

β5

80 β π₯Μ

π(π1 > 80) = π (π§ >

) = π(π§ > 2.79) = 1 β 0.9974 = 0.0026

π

c) Let M2 represent the mean yield rate of 25 plots chosen at random from the field,

According to CLT, what is the mean and standard deviation of M1? And find the

probability of getting the average yield rate greater than 80 lbs.

π₯Μ
= 70 π2 =

π

= 1.6

β25

80 β π₯Μ

π(π2 > 80) = π (π§ >

) = π(π§ > 6.25) = 0

π

d) Does the sample size affect the use ofthe Central Limit Theorem in b) and c)?Why or

why not?

Yes it does, because CLT should be used if the sample size is more than 25.

2. The survival times of guinea pigs inoculated with an infectious viral strain vary from anim...

*flag*Report DMCA

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors