Question

Summer high temperatures are distributed normally with a mean of 99.9 and a standard deviation of 3.7. NOTE: Round your z − score to 2 decimal places before calculating a probability.

What is the summer high temperature that is the 89 th percentile of this distribution? 95.4 104.4 96.6 103.2 None of the above

What is the probability that a randomly selected summer day has a high temperature of 101? 0.3 0 -0.3 0.3821 0.6179

What is the probability that a randomly selected summer day has a high temperature greater than 101? 0 0.6179 -0.3 0.3821 0.3

What is the probability that a randomly selected summer day has a high temperature between 98 and 100? 0.817 0.207 0.54 -0.207 -0.54

A sample is taken from this population and found to have outliers. Which measure of center is the most appropriate to use?

Answer 1

1)

for 89th percentile critical value of z=1.2265

therefore corresponding value=mean+z*std deviation=104.4

2)

probability that a randomly selected summer day has a high temperature of 101 =0

(since point probability on a continuous distribution is zero)

3) probability that a randomly selected summer day has a high temperature greater than 101 :

probability =P(X>101)=P(Z>(101-99.9)/3.7)=P(Z>0.3)=1-P(Z<0.3)=1-0.6179=0.3821

4)

probability that a randomly selected summer day has a high temperature between 98 and 100 :

probability =P(98<X<100)=P((98-99.9)/3.7)<Z<(100-99.9)/3.7)=P(-0.51<Z<0.03)=0.512-0.305=0.2070

5)

since outliers is there, we should use median as a measure of center since it is resistive to outliers