Question

A gardener buys a package of seeds. Seventy-five percent of seeds of this type germinate. The gardener plants 90 seeds. Approximate the probability that the number of seeds that germinate is between 57.5 and 72.5 exclusive.

Answer 1

Mean = n * P = ( 90 * 0.75 ) = 67.5
Variance = n * P * Q = ( 90 * 0.75 * 0.25 ) = 16.875
Standard deviation = = 4.1079

P ( 57.5 < X < 72.5 )
Using continuity correction
P ( n + 0.5 < X < n - 0.5 ) = P ( 57.5 + 0.5 < X < 72.5 - 0.5 ) = P ( 58 < X < 72 )

P ( 58 < X < 72 )
Standardizing the value

Z = ( 58 - 67.5 ) / 4.1079
Z = -2.31
Z = ( 72 - 67.5 ) / 4.1079
Z = 1.1
P ( -2.31 < Z < 1.1 )
P ( 58 < X < 72 ) = P ( Z < 1.1 ) - P ( Z < -2.31 )
P ( 58 < X < 72 ) = 0.8633 - 0.0104
P ( 58 < X < 72 ) = 0.8530