Question

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 86 and estimated standard deviation σ = 35. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

mean = = 86

standard deviation = =35

P( x < 40)

P ( x - / ) < ( 40 - 86 / 35)

P ( z < -46/ 35 )

P ( z < -1.31)

Using z table

=0.0951

Probability = 0.0951

d) n = 5

= u =86

₌ /n  =35/5 = 15.6525

P (   < 40 )

P ( - /) < (40 - 86 / 15.6525)

P ( z < - 46/ 15.6525 )

P ( z < -2.94 )

Using z table

= 0.0016

Probability = 0.0016