assume that in a large population of white pine tress, the lengths of fallen mat
ID: 3126913 • Letter: A
Question
assume that in a large population of white pine tress, the lengths of fallen mature seed cones are normally distributed with mean= 15.4cm and standard deviation =4.5 then,
a)if one such cone is randomly selected, what is the probability that it will be between 10.9cm and 19.9cm long?(no continuity correction)
b)if a sample of three cones is randomly chosen, what is the probability that the sample average cone length will be between 14cm and 16cm long?( no continuity correction?
c)if a sample of five cones is randomly chosen, what is the probability that the sample average cone length will be between 14cm and 16cm long?
e) repeat b but with continuity correction, unit of measurment=1.0cm
'f)repeat b but with continuity correction, unit of measurment=0.5cm
g)repeat c but with continuity correction unite of measurement=0.5cm
h)repeat c but with continuity correction unite of measurement=0.25cm
Explanation / Answer
a)if one such cone is randomly selected, what is the probability that it will be between 10.9cm and 19.9cm long?(no continuity correction)
= P( 10.9 < X < 19.9)
= P( X < 19.9) - P (X < 10.9)
= 0.8413 - 0.1586
= 0.6826
.
b)if a sample of three cones is randomly chosen, what is the probability that the sample average cone length will be between 14cm and 16cm long?( no continuity correction?
= P ( 14 < X < 16)
= P ( X < 16 ) - P (X < 14)
= 0.5913 - 0.2949
= 0.2963
.
c)if a sample of five cones is randomly chosen, what is the probability that the sample average cone length will be between 14cm and 16cm long?
= P ( 14 < X < 16)
= P ( X < 16 ) - P (X < 14)
= 0.6172 - 0.2433
= 0.3738
.
e) repeat b but with continuity correction, unit of measurment=1.0cm
= P ( 14 < X < 16)
= with continuity correction
= P ( 15 < X <15)
= 0
'f)repeat b but with continuity correction, unit of measurment=0.5cm
= P ( 14 < X < 16)
= with continuity correction
= P ( 14.5 < X <15.5)
= 0.1508
.
g)repeat c but with continuity correction unite of measurement=0.5cm
= P ( 14 < X < 16)
= with continuity correction
= P ( 14.5 < X <15.5)
= 0.1924
h)repeat c but with continuity correction unite of measurement=0.25cm
= P ( 14 < X < 16)
= with continuity correction
= P ( 14.25 < X <15.75)
= 0.2851
Hope this helps.
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