Most questions will require you to use either the normalcdf or InvNorm calculato

Question

Most questions will require you to use either the normalcdf or InvNorm calculator function. "Show your work by naming the function and calculator inputs. For example: normalcdf(332, 338, 336,3) 1. On homework 2 you examined a population of commercial chickens whose hatching weights are approximately normally distributed with a mean of 45 grams and standard deviation of 4 grams. a What proportion of chicks have hatching weights between 44 and 46 grams b) What proportion of chicks have hatching weights under 35 grams? c) What is the 20th percentile for chick hatching weights? d) How heavy are the top 15% of chick hatching weights?

Explanation / Answer

Mean = 45

S.D. = 4

a)

P( 44 < X < 46)

Z score at X = 44

Z = (X - ) /
Z = (44 - 45) / 4
Z = -0.25

Z score at X = 46

Z = (X - ) /
Z = (46 - 45) / 4
Z = 0.25

From Z score table

P( 44 < X < 46) = P(-0.25 < Z < 0.25) = 0.1974

b)

P( X < 35)

Z score at X = 35

Z = (X - ) /
Z = (35 - 45) / 4
Z = -2.5

From Z score table

P( X < 35) = P( Z < -2.5) = 0.0062

c)

20th percentile

at a p-value of 0.20 the z score at 0.20 from z score table

Z = -0.842

X at z value

Z = (X - ) /
-0.842 = (X- 45) / 4
X = 45 - 3.368
X = 41.632

d)

P = 1- 0.15 = 0.85

at a p-value of 0.85 the z score at 0.85 from z score table

Z = 1.036

X at z value

Z = (X - ) /
1.036 = (X- 45) / 4
X = 45 + 4.144
X = 49.144

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