Answer:
0.0635 ; 0.1093
Step-by-step explanation:
Given that :
Mean (m) = 181
Standard deviation (s) = 7.3
Height = x
a) The probability that the person is between 160 and 170 centimeters
160 < x < 170
P(x < 160) - P(x< 170)
Z = (170 - 181) / 7.3) ; (160 - 181) / 7.3
Z = - 1.51 ; Z = - 2.88
P(Z < - 1.51) - P(Z < - 2.88)
0.0655 - 0.0020 (from Z table ; first integer of the y axis, decimal point value on the horizontal x axis ; the value at the intersection is the z probability value).
0.0655 - 0.0020 = 0.0635
b) The probability that the person is higher than 190 centimeter
P(x > 190)
Zscore = (x - m) / s
Zscore = (190 - 181) / 7.3
Zscore = 1.23
P(Z > 1.23) = 1 - P(Z < 1.23)
P(Z > 1.23) = 1 - 0.8907
P(Z > 1.23) = 0.1093