1)A variable is normally distributed with mean13 and standard deviation 2. a. Fi

Question

1)A variable is normally distributed with mean13 and standard deviation 2.

a. Find the percentage of all possible values of the variable that lie between 9 and16.

b. Find the percentage of all possible values of the variable that exceed 8.

c. Find the percentage of all possible values of the variable that are less than11

2)Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.31 and standard deviation of 0.18. Find the percentage of preterm infants who have the following arterial cord pH levels.

a. pH levels between 7.00 and 7.50

b. pH levels over 7.39

Explanation / Answer

Mean = 13

Standard deviation = 2

P(X <A) = P(Z < (A - mean)/standard deviation)

a) P(9<X<16) = P(X < 16) - P(X <9)

= P(Z <(16 - 13)/2) - P(Z < (9 - 13)/2)

= P(Z < 1.5) - P(Z < -2)

= 0.9332 - 0.0228

= 0.9104

Percentage of all possible values of the variable that lie between 9 and16 = 91.04%

b) P(X > 8) = 1 - P(X < 8)

= 1 - P(Z <(8-13)/2)

= 1 - P(Z < -2.5)

= 1 - 0.0062

= 0.9938

Percentage of all possible values of the variable that exceed 8 = 99.38%

c) P(X < 11) = P(Z <(11-13)/2)

= P(Z < -1)

= 0.1587

Percentage of all possible values of the variable that are less than11 = 15.87%

NB: Please post different questions separately

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