MA2222 - HW02

MA2222 - HW02 - Department of Mathematics Name:

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Unformatted text preview: Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor's Name: _______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No: ___________________ Willis Thai 5.3-1 Let (a) W{ (b) W{ | | MA2222 be a random sample from a normal distribution W{ % {. % {. % . HW02 {. Compute: % . { . . I | { 3I3 { {. { { . { { { { I 5.3-2 Let X be W{ {. Using the same set of axes, sketch the graphs of the probability density functions of: (a) . (b) , the mean of a random sample of size 9 from this distribution. (c) , the mean of a random sample of size 36 from this distribution. % % . - %% % . | % 3I3 { . - { 5.3-3 5.3-6 If is a random sample of size determine: (a) W 3 X( { X . { 3 . Let X equal the widest diameter (in millimeters) of the fetal head measured between the 16th {. Let be and 25th weeks of pregnancy. Assume that the distribution of X is W{ the sample mean of a random sample of observations of X. (a) Give the values of { { and { {. {I{ % $ % IJ{I{ J (b) Find W{ 33 {. {. { { { . - { { 3I3 % . - % % from the normal distribution W{ {, Willis Thai # $ # MA2222 3 # & HW02 $ #"" $ { % (b) W { 5.3-9 # 3 3 $ # # 3 3 3 X( 3 % . { X . { 3 # & { { # '"{ 3 # $ %" # { % { # . { 3 # $'"" # . % , using $ % , using $ # #"" { 3 { {. 3 {. & { #"" '"{ 3 3 $ %" #"" & #"" { { $'"" #"" Let X equal the force required to pull a stud out of a window that is to be inserted into an automobile. Assume that the distribution of X is W{ ). (a) Find W{ {. . % {I { { { F %% I (b) If is the mean and W is the variance of a random sample of size distribution of X, determine W{ 3 {. %. % {I { { { I %% #$ % ' from this 5.4-4 Approximate W{ 33 from a distribution with mean . # I {. & I (c) Find constants a and b so that W 3 W 3 J. J. { % I3 I3 3 IF 3 $ $ % ,I % % % I{ . % { % 3 3 { 5.4-5 be a random sample of size 18 from a chi-square distribution with . Let . Recall that , (a) How is X distributed? X( $ $ I { {, % $ { { { %{ { (b) Using the result of part (a), we see from Table IV in the Appendix that W{ 3 { and W{ 3 . Compare these two probabilities with the approximations found using the central limit theorem. I { { { . - { I {, where is the mean of a random sample of size 32 . and variance % . F { %% % . % % Willis Thai 5.4-8 MA2222 HW02 { { Let X equal the weight in grams of a miniature candy bar. Assume that { { and . Let be the sample mean of a random sample of bars. Find: (a) { {. {I{ (b) { {. (c) W{ % IJ{I{ . J $ candy 33 5.4-12 A church has pledges (in dollars) with a mean of 2000 and a standard deviation of 500. A random sample of size is taken from all of this church's pledges and the sample mean is considered. Approximate W{ 2 {. . # { I2 . { % I2$ '"" ' . - % {, approximately. % . {. % 3 I 3 3I3 F { { { . - { % { 5.4-18 Assume that the sick leave taken by the typical worker per year has , , measured in days. A firm has employees. Assuming independence, how many sick days should the firm budget if the financial officer wants the probability of exceeding the budgeted days to be less than 20%? {I 4 { . F I4 % . % % 208 Days 5.5-3 A public opinion poll in Southern California was conducted to determine whether Southern Californians are prepared for the big earthquake that experts predict will devastate the region sometime in the next 50 years. It was learned that "60% have not secured objects in their homes that might fall and cause injury and damage during a temblor." In a random sample of Southern Californians, let equal the number who "have not secured objects in their homes." Find W{ 3 3 {, approximately. % .% 0 % .% 0 {. % 3 I 3 3I3 F %{ % 0 0 % 0 0 { %{ . - { %{ %% . - % % % Let X equal the number out of mature aster seeds that will germinate when is the probability that a particular seed germinates. Approximate W{ 3 3 {. 5.5-4 Willis Thai %0 0 { { . - { . %0 3I3 { MA2222 %0 0 . % . %0 F {. 3I3 { HW02 5.5-9 Let X equal the number of alpha particles emitted by barium-133 per second and counted by a Geiger counter. Assume that X has a Poisson distribution with . Approximate { W{ I {I{ %, IJ{I{ % % . % . % {. { { { . - { { I F 3I3 % . % % 5.5-19 The number of trees in one acre has a Poisson distribution with mean 60. Assuming {, where X is the number of independence, compute approximately W{ 3 3 trees in 100 acres. ...
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