Question

Assume X = systolic blood pressure of a healthy adult aged 21-45 where X is assumed to be normally distributed with  = 120 and σ = 20. a. Find the probability that a randomly selected person from this population has systolic blood pressure less than 140, ie find P(X < 140).
b. If 10% of the population have "high" systolic blood pressure, find the borderline point between "normal" and "high", ie find x0 such that P(X > x0) = .10.
c. A friend claims the graduate students in the sciences at x have a true mean systolic blood pressure of higher than 120. A random sample of 16 x science graduate students has a mean of 135 (ie x̅ = 135). What is the probability of obtaining a sample mean of 135 or higher when in fact, their population has =120, ie find P(X ≥ 135 |  = 120 and σ = 20)? What do you conclude?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	120
std deviation   =σ=	20.0000

probability =

P(X<140)

=

P(Z<1)=

0.8413

b)

for top 10%; crtical z =1.28

therefore corresponding value=mean+z*std deviation=

145.60

c)

sample size       =n=	16
std error=σx̅=σ/√n=	5.0000

probability =

P(Xbar>135)

=

P(Z>3)=

1-P(Z<3)=

1-0.9987=

0.0013