Question

Assume that the cholesterol levels for adults are normally distributed with mean cholesterol level of 51.5 mg/dL and standard deviation of 14.3 mg/dL. Find the probability that an individual will have a cholesterol level

a.) 60 mg/dL, at least

b.) 40 mg/dL, at most

c.) Between 40 and 60 mg/dL

PLZ show work :)

Answer 1

Solution :

Given that ,

mean = = 51.5

standard deviation = = 14.3

(a)

P(x 60) = 1 - P(x   60)

= 1 - P[(x - ) / (60 - 51.5) / 14.3]

= 1 -  P(z 0.59)  

= 0.2776

(b)

P(x 40)

= P[(x - ) / (40 - 51.5) / 14.3]

= P(z -0.80)

= 0.2119

(c)

P(40 < x < 60) = P[(40 - 51.5)/ 14.3) < (x - ) /  < (60 - 51.5) / 14.3) ]

= P(-0.80 < z < 0.59)

= P(z < 0.59) - P(z < -0.80)

= = 0.7224 - 0.2119

= 0.5105