Question

According to one​ association, the total energy needed during pregnancy is normally​ distributed, with mean

μ=2600

kca / day

and standard deviation

σ=50

kca l day

​(a) Is total energy needed during pregnancy a qualitative variable or a quantitative​ variable?

​(b) What is the probability that a randomly selected pregnant woman has an energy need of more than 2625

StartFraction kca l Over day EndFractionkcalday​?

Interpret this probability.​(c) Describe the sampling distribution of

x overbarx​,

the sample mean daily energy requirement for a random sample of 20 pregnant women.​(d) What is the probability that a random sample of 20 pregnant women has a mean energy need of more than 2625

kca / day ​?

Interpret this probability.

​(a) Choose the correct answer below.

Qualitative

Quantitative

​(b)

​ P(X>​2625)=

Answer 1

Answer:

a)

Total energy needed during pregnancy is a quantitative variable

b)

The probability is: P(X>2625) =
=P((X-mean)/s >(2625-2600)/50)
=P(Z>0.5) =1 - P(Z<0.5)
=0.3085 (Using standard normal table)

c)

Sample mean = 2,600
Sample standard deviation= s/vn
=50/sqrt(20)
=11.18034 = 11.18

X ~ (2600, 11.18)

d)

The probability is: P(xbar>2625) =
=P((xbar-mean)/(s/vn) >(2625-2600)/(50/sqrt(20)))
=P(Z> 2.24) = 1 - P(Z< 2.24)
=0.0126 (Using standard normal table)