Question

Big chickens: A report from a poultry industry news Web site stated that the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1395 grams and standard deviation 200 grams. Use the TI-84 PLUS calculator and round your answers to at least two decimal places (a) Find the 31" percentile of the weights. (b) Find the 87 percentile of the weights. (c) Find the first quartile of the weights. (d) A chicken farmer wants to provide a money-back guarantee that his broilers will weigh at least a certain amount. What weight should he guarantee so that he will have to give his customers' money back only 1% of the time? Part 1 of 4 Find the 31" percentile of the weights. The 31" percentile of the broiler weights is 1295.83 grams. Part: 1/4 Part 2 of 4 Find the 87 percentile of the weights. The 87" percentile of the broiler weights is grams.

Answer 1

Solution:

Given:

Mean =

μ = 1395

Standard deviation =

0 = 200

Part b) 87^th percentile of weights:

Use following steps in TI 84 plus calculator:

Press 2ND and VARS

select invNorm(

TI-84 Pius Silver Edition TEXAS INSTRUMENTS DISTR DRAW 1: normalpdf 2: normalcdfc invNorma 4. iFT 5: tpdf 6:tcdf 7*X2 pdf STAT PLOT F1 TBLSETF2 FORMATS CALC F4 WINDOWZOOMTRACE TABLE F5 GRAPH 2ND MODE

Enter numbers:

TI-84 Plus Silver Edition TEXAS INSTRUMENTS invlor area:.87 .: 1395 o: 200 Paste STAT PLOTF1 TBLSETE2 FORMAT ES WINDOW ZOOM CALC F4 TRACE TABLE F5 GRAPH QUIT 2ND GO ALPHA [email protected] MATH MA ANGLE APPS PRGM VARS VARS CLEAR

Click on Paste and press Enter two times

TI-84 Plus Silver Edition TEXAS INSTRUMENTS invNormc.87: 139! 1620.278226 STAT PLOTF1 TBLSET F2 FORMAT F3 CALC 54 WINDOW ZOOM TRACE TABLE F5 GRAPH 2ND MODE DEL ALPHA X.T.en STAT

87^th percentile is : 1620.28

Part c) First quatile Q1:

For Q1, P( X < Q1) = 0.25

thus we use same steps , just change the Area to 0.25

thus we get:

TI-84 Plus Silver Edition TEXAS INSTRUMENTS invNorm(0.25, 13' 1260.10205 STAT PLOTF1 TBLSETE FORMAT E WINDOW ZOOM CALC F4 TRACE TABLE F5 GRAPH 2ND MODE DEL ALPHA [email protected] STAT DIETE MATH ANOLES ADDE ARALE VADS CLEAR

First Quartile Q1 = 1260.10

Part d) Find x value for lowest 1% area.

Thus use same steps and enter Area = 0.01

TI-84 Plus Silver Edition TEXAS INSTRUMENTS invNorm(0.01.13 929.7304246 TABLE F5 STAT PLOTF1 TBLSETF2 FORMAT ES WINDOW ZOOM CALC F4 TRACE GUT 2ND DEN ALPHA ΜΑΤΗ ANGLEDD APPS PRGM DISE VARS CLEAR

thus x = 929.73