Question

# Use the empirical rule to answer question. Please draw a picture with all the percentages as...

Use the empirical rule to answer question. Please draw a picture with all the percentages as well. Suppose the average age for a professional soccer player is 25 years with a standard deviation of 4 years. Assume that this distribution follows a normal distribution.

a. Approximately what percentage of pro soccer players are between the ages of 21 and 25?

b. Approximately what percentage of pro soccer players are between the ages of 21 and 29?

c. Approximately what percentage of pro soccer players are greater than age 33?

d. Approximately what percentage of pro soccer players are between the ages of 17 and 21?

here we use standard normal variacte z=(x-mean)/sd

(a)required percentage=34.13

for x=21, z=(21-25)/4=-1

for x=25, z=(25-25)/4=0

P(21<X<25)=P(-1<Z<0)=P(Z<0)-P(Z<-1)=0.5-0.1587=0.3413

(b)required percentage=68.26

for x=21, z=(21-25)/4=-1

for x=29, z=(29-25)/4=1

P(21<X<29)=P(-1<Z<1)=P(Z<1)-P(Z<-1)=0.8413-0.1587=0.6826

(c) required percentage=2.27

for x=33, z=(33-25)/4=2

P(X>2)=1-P(Z<2)=1-0.9773=0.0227

(d) required percentage=13.59%

for x=21, z=(21-25)/4=-1

for x=17, z=(17-25)/4=-2

P(17<X<21)=P(-2<Z<-)=P(Z<-2)-P(Z<-1)=0.1587-0.0228=0.1359

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• Statistics Discussion: The accuracy of a forecasting technique is evaluated especially using the MSE (mean squared...
• If the U.S. government manages to close a recessionary gap and achieve potential GDP with fiscal...
• A block with mass 10kg is on a ramp angled at 20 degrees above the horizontal,...
• I have a sample of 31 7thgrade girls who took an IQ test.  I calculated the sample...
• A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
• Brick column in the external corridor of a house, with section size of 440 mm X520...