Respuesta :
Answer:
Step-by-step explanation:
A bell shaped distribution means that it is a normal distribution.
Let x be a random variable representing the blood platelet count of the group of women. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 255.4
σ = 61.3
a) the probability that a woman has platelet counts between 181.5 and 320.1 is expressed as
P(181.5 ≤ x ≤ 320.1)
For x = 181.5,
z = (181.5 - 255.4)/61.3 = - 1.21
Looking at the normal distribution table, the probability corresponding to the z score is 0.11
For x = 320.1
z = (320.1 - 255.4)/61.3 = 1.06
Looking at the normal distribution table, the probability corresponding to the z score is 0.86
Therefore,
P(181.5 ≤ x ≤ 320.1) = 0.86 - 0.11 = 0.75
The percentage of percentage of women with platelet counts within 1 standard deviation of the mean, or between 181.5 and 320.1 is
0.75 × 100 = 75%
b) the probability that a woman has platelet counts between 112.2 and 389.4 is expressed as
P(112.2 ≤ x ≤ 389.4)
For x = 112.2,
z = (112.2 - 255.4)/61.3 = - 2.34
Looking at the normal distribution table, the probability corresponding to the z score is 0.0096
For x = 389.4
z = (389.4 - 255.4)/61.3 = 2.19
Looking at the normal distribution table, the probability corresponding to the z score is 0.9857
Therefore,
P(112.2 ≤ x ≤ 389.4) = 0.9857 - 0.0096 = 0.9761
The percentage of percentage of women with platelet counts within 1 standard deviation of the mean, or between 112.2 and 389.4 is
0.9761 × 100 = 96.71%
