Question

The weights of New Zealand hamsters are normally distributed with mean 63.5 g and standard deviation 12.2 g.

a. What is the probability a randomly selected New Zealand hamster weighs more than 74g? Copy-and-paste the R command and its return into your assignment.

b. 35% of all New Zealand hamsters weigh less than x grams. What is the number x? Copy-and-paste the R command and its return into your assignment.

c. If there are 1000 weights in this population, how many of them do you expect will be 78 g or greater? Use R to find the expected number. You will need more than one R command. Copy-and-paste the R commands and their returns into your assignment.

d. Find two symmetric values a and b such that P(a < X < b) = 0.99. symmetric values are equally distant from the mean. You will need more than one R command. Copy-andpaste the R commands and their returns into your assignment.

Answer 1

Solution:

Weights are normally distributed.

Mean = 63.5

SD = 12.2

Part a

We have to find P(X>74)

P(X>74) = 1 – P(X<74)

Required R commands are given as below:

> Req.prob = 1 - pnorm(74,63.5,12.2)

> Req.prob

[1] 0.1947138

Answer: 0.1947

Part b

Here, we have to find x such that P(X<x) = 0.35

Required R commands are given as below:

> x = qnorm(0.35,63.5, 12.2)

> x

[1] 58.79909

Answer: 58.7991

Part c

Required R commands are given as below:

> prob. = 1 - pnorm(78,63.5,12.2)

> n = 1000

> exp.number = n*prob.

> exp.number

[1] 117.3134

Answer: 117.3134

Part d

Required R commands are given as below:

> p1 = (1 - 0.99)/2

> p2 = 0.99+p1

> a = qnorm(p1,63.5,12.2)

> b = qnorm(p2,63.5,12.2)

> a

[1] 32.07488

> b

[1] 94.92512

a = 32.07488

b = 94.92512