4 questions about statistics/probability: A study was performed on hemoglobin levels

[Khrazer]

Hi. I'm having trouble solving some problems:


A study was performed on hemoglobin levels (measured in g/dl) in 2000 women. This study revealed that:
Hemoglobin limits have normal distributional behavior; that half of the women had hemoglobin levels below 12 g/dl; and 4.95% of the women studied had hemoglobin levels greater than 14 g/dl.
Considering adult and healthy women:
A) What is the mean and variance of the random variable that measures your hemoglobin levels?
B) Calculate a probability that your own hemoglobin levels are less than 10.5 g / dl.
C) Calculate a probability that your own hemoglobin levels are between 11 and 16 g / dl.
D) Calculate the percentile 10% of hemoglobin levels in these women.

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A) Considering X is the random variable, I understand the probability of X<12=0.5 . Does that mean the Mean is 12? If so, how do I get the variance from here?
B) I have no idea what to do here
C) I have no idea what to do here
D) If this case has a "normal distributional behavior", that means that percentile 5% has hemoglobin levels <10 , right? In that case, percentile 10% has more ~0.225 g/dl than percentile 5%. (I tried to figure out the hemoglobin difference between each 1% percentile, by dividing taking the difference between percentile 50% and 95%(I assume thats 14g/dl given on the problem) and then dividing it)

I'm feeling like I did something wrong on D)

Can anyone help me? Thank you for your time!

 

[ksdhart2]

Hi. I'm having trouble solving some problems:


A study was performed on hemoglobin levels (measured in g/dl) in 2000 women. This study revealed that:
Hemoglobin limits have normal distributional behavior; that half of the women had hemoglobin levels below 12 g/dl; and 4.95% of the women studied had hemoglobin levels greater than 14 g/dl.
Considering adult and healthy women:
A) What is the mean and variance of the random variable that measures your hemoglobin levels?
B) Calculate a probability that your own hemoglobin levels are less than 10.5 g / dl.
C) Calculate a probability that your own hemoglobin levels are between 11 and 16 g / dl.
D) Calculate the percentile 10% of hemoglobin levels in these women.

---

A) Considering X is the random variable, I understand the probability of X<12=0.5 . Does that mean the Mean is 12? If so, how do I get the variance from here?
B) I have no idea what to do here
C) I have no idea what to do here
D) If this case has a "normal distributional behavior", that means that percentile 5% has hemoglobin levels <10 , right? In that case, percentile 10% has more ~0.225 g/dl than percentile 5%. (I tried to figure out the hemoglobin difference between each 1% percentile, by dividing taking the difference between percentile 50% and 95%(I assume thats 14g/dl given on the problem) and then dividing it)

I'm feeling like I did something wrong on D)

Can anyone help me? Thank you for your time!

For part A, you're correct that the mean is 12, but your reasoning is flawed. If all you knew was that hemoglobin levels formed a random variable, then you couldn't find the mean. It's specifically because hemoglobin levels are specified as being normally distributed that you know that the mean is the score below which 50% of the scores fall

For the rest, what has your class recently been learning about z-distributions and z-scores? For instance, using the given fact that "4.95% of the women studied had hemoglobin levels greater than 14 g/dl" and [URL="http://http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf]consulting a z-table[/URL] tells me that 14 g/dl is equivalent to a z-score of 1.65. Where does that lead you?