##### Question

In: Statistics and Probability

# Let x be a random variable that represents the level of glucose in the blood (milligrams...

## Solutions

##### Expert Solution

Solution :

Given that ,

mean = = 51

standard deviation = = 47

a) P(x < 40) = P[(x - ) / < (40 - 51) / 47]

= P(z < -0.23)

Using z table,

= 0.4090

b) n = 2  = = 51  = / n = 47/ 2 = 33.23

The probability distribution of x is approximately normal with μx = 51 and σx = 33.23

P( < 40) = P(( -  ) /  < (40 - 51) / 33.23)

= P(z < -0.33)

Using z table

= 0.3707

c) n = 3  = = 51  = / n = 47/ 3 = 27.14

The probability distribution of x is approximately normal with μx = 51 and σx = 27.14

P( < 40) = P(( -  ) /  < (40 - 51) / 27.14)

= P(z < -0.41)

Using z table

= 0.3409

d) n = 5  = = 51  = / n = 47/ 5 = 21.02

The probability distribution of x is approximately normal with μx = 51 and σx = 21.02

P( < 40) = P(( -  ) /  < (40 - 51) / 21.02)

= P(z < -0.52)

Using z table

= 0.3015

e) yes,

The more tests a patient completes, the weaker is the evidence for excess insulin

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