Question

According to the U.S. Census Bureau, the mean per capita income in Texas is $25840, whereas the mean per capita income in Florida is $26560. Suppose both distributions are normal, each with a standard deviation of $8000. Suppose the samples of 100 residents of each state are taken.

Find the probability that the sample mean per capita income in Texas will exceed $27600.

Find the probability that the sample mean per capita income in Florida will exceed $27600

Answer 1

Solution :

Given that ,

mean = = 25480

standard deviation = = 8000

n = 100

= 25480 and

= / n = 8000 / 100 = 8000 / 10 = 800

P( > 27600) = 1 - P( < 27600)

= 1 - P(( - ) / < (27600 - 25480) / 800)

= 1 - P(z < 2.65)

= 1 - 0.996

= 0.004

Probability = 0.004

For florida

mean = = 26560

P( > 27600) = 1 - P( < 27600)

= 1 - P(( - ) / < (27600 - 26560) / 800)

= 1 - P(z < 1.3)

= 1 - 0.9032

= 0.0968

Probability = 0.0968