Answer:
a) 15.866%
b) Middle 95% = 350 ml to 750 ml
c) 0.3829
d) Middle 90% of men’s bladder fall = 385.5ml to 714.5 ml
Explanation:
We solve using z score formula
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.
The distribution of bladder volume in men is approximately Normal with mean 550 ml and standard deviation 100 ml.
Required:
a. What percent of men have a bladder volume smaller than 450 ml?
z = 450 - 550/100
= -1
P-value from Z-Table:
P(x<450) = 0.15866
Convert to percentage
0.15866 × 100
= 15.866%
b. Between what volumes do the middle 95% of men’s bladders fall?
Middle 95% falls between 2 standard deviation of the mean
μ ± 2σ
μ - 2σ
550 - 2(100)
= 550 - 200
= 350 ml
μ + 2σ
= 550 + 2(100)
= 550 + 200
= 750 ml
Middle 95% = 350 ml to 750 ml
c. What proportion of male bladders are between 500 and 600 ml?
For 500ml
z = 500 - 550/100
= -0.5
Probability value from Z-Table:
P(x = 500) = 0.30854
For 600ml
z = 600 - 550/100
= 0.5
Probabilty value from Z-Table:
P(x = 600) = 0.69146
Proportion of male bladders are between 500 and 600 ml
P(x = 600) - P(x = 500)
0.69146 - 0.30854
= 0.38292
≈ 0.3829
d. What volumes do the middle 90% of men’s bladder fall?
The z score for middle 90% + / – 1.645
Hence,
1.645 = x - 550/100
1.645 × 100 = x - 550
164.5 + 550 = x
x = 714.5 ml
-1.645 = x - 550/100
-1.645 × 100 = x - 550
- 164.5 + 550 = x
x = 385.5ml
Middle 90% of men’s bladder fall = 385.5ml to 714.5 ml