Question No. 1

According to The World Bank, only 25% of the population of a certain country had access to electricity as of 2019. Suppose we randomly sample 150 people in Uganda. Let X = the number of people who have access to electricity.

a)What is the probability distribution for X?

b)Find the probability that 15 people in the sample have access to electricity.

c)Find the probability that at most ten people in the sample have access to electricity.

d)Find the probability that more than 25 people in the sample have access to electricity.

Question No. 2

According to media research, in certain country people are reading in average about 200 hours in the last year. This is down from 300 hours five years earlier. Assume the number of hours spent reading follows a normal probability distribution with a standard deviation of 10 hours.

a)What is the probability that a selected person read between 190 and 210 hours per year?

b)What is the probability that a selected person read more than 220 hours per year?

c)If a person is in the top 10% in terms of reading time, how many hours does he read per year?

d)Assume that the distribution of times five years earlier also follows the normal probability distribution with a standard deviation of 8 hours. How many hours did the 1% read per year?

Question No. 3

In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.5 hours per week playing organized sports. The population's standard deviation is 2.2 hours per week. Based on a sample of 121 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.

a)Compute the standard error of the sample mean.

b)What is the chance HLI will find a sample mean between 5 and 6 hours?

c)Calculate the probability that the sample mean will be between 5.3 and 5.7 hours.

d)How strange would it be to obtain a sample mean greater than 6.5 hours?

Question No. 4

The Kentucky Derby is held the first Saturday in May at Churchill Downs in Louisville, Kentucky. The race track is one and one-quarter miles. The following table shows the winners 1990-2011, their margin of victory, the winning time, and the payoff on a $2 share.

Winning Margin Winning Time Payoff on a Year Winner (lengths) (minutes) $2 Win Bet 1990 Unbridled 3.5 2.03333 10.80 1991 Strike the Gold 1.75 2.05000 4.80 1992 Lil E. Tee Sea Hero 1 2.05000 16.80 1993 2.5 2.04000 12.90 1994 Go For Gin 2 2.06000 9.10 1995 Thunder Gulch 2.25 2.02000 24.50 1996 Grindstone nose 2.01667 5.90 1997 Silver Charm 2.04000 4.00 1998 Real Quiet 2.03667 8.40 1999 Charismatic neck 2.05333 31.30 2000 Fusaichi Pegasus 1.5 2.02000 2.30 [continued) Winning Margin Winning Time Payoff on a Year Winner (lengths) (minutes) $2 Win Bet 2001 Monarchos 4.75 1.99950 10.50 2002 War Emblem 2.01883 20.50 2003 Funny Cide 1.75 2.01983 12 80 2004 Smarty Jones 2.75 2.06767 4.10 2005 Giacomo 0.5 2 04583 50.30 2006 Barbaro 2.02267 6. 10 2007 Street Sense 2.25 2.03617 4.90 2008 Big Brown 4 75 2 03033 16.80 2009 Mine That Bird 16.75 2 04433 103 20 2010 Super Saver 2.50 18.00 2011 Animal Kingdom 275 2.034 43.80