The distribution of bladder volume in men is approximately Normal with mean 600

Question

The distribution of bladder volume in men is approximately Normal with mean 600 ml and standard deviation 100 ml. Use the 68-95-99.7 rule to answer parts (a) and (b).

NEED C, D, F, and C(bottom).

(a) Between what values do the middle 95% of men's bladders fall?
400 and 800
(b) What percent of men's bladders have a volume larger than 700 ml? Please use 2 decimal places.
16%

(c) What proportion of male bladders are larger than 550 ml? Please use 2 decimal places.
_________

(d) What proportion of male bladders are between 550 and 650 ml?Please use 2 decimal places.
__________

The distribution of bladder volume in women is approximately Normal with mean 430 ml and standard deviation 60 ml. Use the 68-95-99.7 rule to answer parts (e) and (f).

(e) Between what values do almost all (99.7%) of women's bladder volumes fall?
250 and 610

(f) How small are the smallest 2.5% of all bladders among women?
__________

(c) What proportion of women's bladders have a volume between 500 and 600 ml? Please use 2 decimal places.

___________

Explanation / Answer

mean = 600 and sd = 100

(c) What proportion of male bladders are larger than 550 ml? Please use 2 decimal places.

we shall first calculate the z score for the data as

Z = (X - Mean)/SD

= (550 - 600)/100 = -0.5

now we need to find P(Z>-0.5) , using the z table as

P ( Z>0.5 )=P ( Z<0.5 )=0.6915

(d) What proportion of male bladders are between 550 and 650 ml?Please use 2 decimal places.

we shall first calculate the z score for the data as

Z = (X - Mean)/SD

= (550 - 600)/100 = -0.5

and

we shall first calculate the z score for the data as

Z = (X - Mean)/SD

= (650 - 600)/100 = 0.5

To find the probability of P (0.5<Z<0.5), we use the following formula:

P (0.5<Z<0.5 )=P ( Z<0.5 )P (Z<0.5 )

P ( Z<0.5 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=0.5 we have:

P ( Z<0.5)=1P ( Z<0.5 )

We see that P ( Z<0.5 )=0.6915 so,

P ( Z<0.5)=1P ( Z<0.5 )=10.6915=0.3085

At the end we have:

P (0.5<Z<0.5 )=0.383

NOW

mean = 430 and sd 60

(f) How small are the smallest 2.5% of all bladders among women?

here we shal have to first find the z score for p = 0.025 , which is -1.96

putting it in the z score value

Z = (X-430)/60

X = -1.96*60+430 = 312.4

(c) What proportion of women's bladders have a volume between 500 and 600 ml? Please use 2 decimal places.

we shall first calculate the z score for the data as

Z = (X - Mean)/SD

= (500 - 430)/60 = 1.166

and

(600 - 430)/60 = 2.833

To find the probability of P (1.166<Z<2.833), we use the following formula:

P (1.166<Z<2.833 )=P ( Z<2.833 )P (Z<1.166 )

We see that P ( Z<2.833 )=0.9977

We see that  P ( Z<1.166 )=0.879.

At the end we have:

P (1.166<Z<2.833 )=0.1187

Hope this helps !!

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