Respuesta :
Answer:
(a)0.3493
(b) 0.7611
(c) 0.5034
(d) No it is not unusual
Step-by-step explanation:
Using the TI-84 Plus calculator to answer the following
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Mean 11.8 pounds and Standard deviation 3.1 pounds.
(a) What proportion of babies weigh more than 13 pounds?
z = (x-μ)/σ
= 13 - 11.8/3.1
= 0.3871
Probability value from Z-Table:
P(x<13) = 0.65066
P(x>13) = 1 - P(x<13) = 0.34934
The proportion of babies weigh more than 13 pounds is 0.3493
(b) What proportion of babies weigh less than 14 pounds?
z = (x-μ)/σ
= 14 - 11.8/3.1
= 0.70968
Probability value from Z-Table:
P(x<14) = 0.76105
The proportion of babies weigh less than 14 pounds is 0.7611
(c) What proportion of babies weigh between 11 and 15.8 pounds?
For x = 11
z = (x-μ)/σ
= 11 - 11.8/3.1
= -0.25806
Probability value from Z-Table:
P(x = 11) = 0.39818
For x = 15.8
z = (x-μ)/σ
= 15.8 - 11.8/3.1
= 1.29032
Probability value from Z-Table:
P(x = 15.8) = 0.90153
The proportion of babies weigh between 11 and 15.8 pounds
P(x = 15.8) - P(x = 11)
= 0.90153 - 0.39818
= 0.50335
≈ 4 decimal places = 0.5034
(d) Is it unusual for a baby to weigh more than 18 pounds?
z = (x-μ)/σ
= 18 - 11.8/3.1
= 2
Probability value from Z-Table:
P(x≤ 18) = P(x = 18) =
0.97725
No it is not unusual to have a Weight of 18 pounds
Round the answers to four decimal places.
(a) The proportion of babies weigh more than 13 pounds is 0.3493.
(b) The proportion of babies weigh less than 14 pounds is 0.7611.
(c) The proportion of babies weigh between 11 and 15.8 pounds is 0.5034.
(d) No, it is not unusual.
"To understand the calculation, check below."
Probability
Formula:
z = (x-μ)/σ,
x is the raw score.
μ is the population mean.
σ is the population standard deviation.
Mean = 11.8 pounds
Standard deviation =3.1 pounds.
Part (a) :
The proportion of babies weigh more than 13 pounds is :
z = (x-μ)/σ
z = 13 - 11.8/3.1
z = 0.3871
Probability value from Z-Table:
P(x<13) = 0.65066
P(x>13) = 1 - P(x<13) = 0.34934
The proportion of babies weigh more than 13 pounds is 0.3493
Part (b):
The proportion of babies weigh less than 14 pounds is :
z = (x-μ)/σ
z= 14 - 11.8/3.1
z= 0.70968
Probability value from Z-Table:
P(x<14) = 0.76105
The proportion of babies weigh less than 14 pounds is 0.7611.
Part (c):
The proportion of babies weigh between 11 and 15.8 pounds is :
For x = 11
z = (x-μ)/σ
z= 11 - 11.8/3.1
z= -0.25806
Probability value from Z-Table:
P(x = 11) = 0.39818
For x = 15.8
z = (x-μ)/σ
z= 15.8 - 11.8/3.1
z= 1.29032
Probability value from Z-Table:
P(x = 15.8) = 0.90153
The proportion of babies weigh between 11 and 15.8 pounds:
P(x = 15.8) - P(x = 11)
= 0.90153 - 0.39818
= 0.50335
≈ 4 decimal places = 0.5034
Part (d) :
Is it unusual for a baby to weigh more than 18 pounds :
z = (x-μ)/σ
z = 18 - 11.8/3.1
z = 2
Probability value from Z-Table:
P(x≤ 18) = P(x = 18) =0.97725
No, it is not unusual to have a Weight of 18 pounds.
Learn more about "Mean weight":
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