Respuesta :
Answer:
[tex]P(3.9<X<5)=P(\frac{3.9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{5-\mu}{\sigma})=P(\frac{3.9-4.8}{0.3}<Z<\frac{5-4.8}{0.3})=P(-3<z<0.67)[/tex]
[tex]P(-3<z<0.67)=P(z<0.67)-P(z<-3)[/tex]
[tex]P(-3<z<0.67)=P(z<0.67)-P(z<-3)=0.748571-0.00135=0.74722[/tex]
d. .7462
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(4.8,0.3)[/tex]
Where [tex]\mu=4.8´[/tex] and [tex]\sigma=0.3[/tex]
We are interested on this probability
[tex]P(3.9<X<5.0)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(3.9<X<5)=P(\frac{3.9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{5-\mu}{\sigma})=P(\frac{3.9-4.8}{0.3}<Z<\frac{5-4.8}{0.3})=P(-3<z<0.67)[/tex]
And we can find this probability with this difference:
[tex]P(-3<z<0.67)=P(z<0.67)-P(z<-3)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-3<z<0.67)=P(z<0.67)-P(z<-3)=0.748571-0.00135=0.74722[/tex]
And on this case the most accurate answer would be:
d. .7462
Answer: option d is the correct answer.
Step-by-step explanation:
For healthy females, x has a approximately normal distribution. We would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = red blood counts.
µ = mean count
σ = standard deviation
From the information given,
µ = 4.8
σ = 0.3
We want to find the that a healthy female has a red blood count between 3.9 and 5.0. It is expressed as
P(3.9 ≤ x ≤ 5) = P(x ≤ 5) - P(x ≤ 3.9)
For x = 3.9,
z = (3.9 - 4.8)/0.3 = - 3
Looking at the normal distribution table, the probability corresponding to the z score is 0.00135
For x = 5,
z = (5 - 4.8)/0.3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.7486
P(3.9 ≤ x ≤ 5) = = 0.7486 - 0.00135
= 0.747
