Can anyone help me with these questions? Thank you. Male Angus beef cattle weigh

Question

Can anyone help me with these questions? Thank you.

Male Angus beef cattle weights are distributed N(1156, 120) (in Ibs.). If we randomly sample 36 male Angus cows, what is the probability that their average weight will be 1199 lbs. or more? Use Minitab to solve this by inputting the actual sampling distribution parameters, then use Minitab to show that the probability obtained by using the corresponding standardized score is the same. +' If we randomly sample 64 male Angus cows, what is the probability that their average weight will be 1199 lbs. or more? Use Minitab to solve this inputting the actual sampling distribution parameters, then use Minitab to show that the probability obtained by using the corresponding standardized score is the same. 1. a. b. According to the US Census Bureau, commuting times for Indiana residents have a mean of 24 minutes and a population standard deviation of 12 minutes. If one Indiana resident is selected at random, what is the approximate probability that his/her commute time is less than 18 minutes? (Hint: Are we able to use the CLT in this problem to get a sampling distribution?) If 36 Indiana residents are selected at random, what is the approximate probability that 2. a. b. ir average commute time will be less than18 minutes?

Explanation / Answer

2

given that

mean = 24
and sd = 12

a)

we know that z score is given as

z = (x-mean)/(sd)

= here x = 18

(18-24)/12 = -0.5

we check the z table for P(Z<-0.5)

P ( Z<0.5 )=1P ( Z<0.5 )=10.6915=0.3085

b) for n = 36

we calculate the z score as

z = (x-mean)/(sd/sqrt(n))

= (18-24)/(12/sqrt(36))

P ( Z<3 )=1P ( Z<3 )=10.9987=0.0013

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