Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.8 pounds and standard deviation 3.1 pounds. Use the TI-84 Plus calculator to answer the following. (a) What proportion of babies weigh more than 13 pounds? (b) What proportion of babies weigh less than 14 pounds? (c) What proportion of babies weigh between 11 and 15.8 pounds? (d) Is it unusual for a baby to weigh more than 18 pounds? Round the answers to four decimal places.

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."

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.

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