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.
