Question

A particular county in Texas has 21% unemployment rate. A random sample of 58 county residents is selected monthly in order to monitor county’s unemployment rate. What is the probability that unemployment rate among these residents is over 16%? (Round your answer to 4 digits after the decimal point).

a) 0.1749

b) 0.5489

c)0.8251

d) none

Answer 1

Solution:

Given ,

p = 21% = 0.21 (population proportion)

n = 58 (sample size)

Let be the sample proportion.

The sampling distribution of is approximately normal with

mean = =  p = 0.21

SD =   =     

=

=  0.05348219168

Now ,

P[ is over 16% ]

= P[ > 0.16]

=

=  P(Z > (0.16 -0.21)/0.05348219168)

= P(Z > -0.935)

= 1 - P[Z < -0.935]

= 1 - 0.1749   ...use z table

= 0.8251

Answer :  0.8251