Question

The mass of an object is normally distributed with a mean of μ = 3480 grams and a standard deviation of σ = 550 grams. Find the 28th percentile in this population.

a. 3161 grams

b. 2834 grams

c. 3050 grams

d. 2824 grams

Part B.) If five objects from the population are randomly selected, what is the probability the mean mass among them is less than 3229 grams?

a.) 0.1539

b.) 0.4020

c.) 0.546

d.) 0.0250

Answer 1

Given that,

mean = = 3480

standard deviation = = 550

Using standard normal table,

P(Z < z) = 28%

= P(Z < z) = 0.28  

= P(Z <-0.58 ) = 0.28

z =-0.58 Using standard normal z table,

Using z-score formula  

x= z * +

x=-0.58*550+3480

x= 3161

b

n=5

= 3480

=  / n = 550/ 5=245.97

P( < 3229) = P[( - ) / < ( 3229-3480) / 245.97]

= P(z < -1.02)

Using z table  

= 0.1539