Answer:
Given:
X = 149
Mean, u = 146
Standard deviation
= 2.3
a) Let's find the zscore at x = 149

From the standard normal table
NORMSDIST(1.3043) = 0.9039
Therefore
P(x>149) = P(z> 1.3043)
= 1 - 0.90393
= 0.0961
The probability that the baseball is within regulation weight is
1 - 0.0961 = 0.9039
b) Let's use binomial distribution,
Given :
n = 16
p = 0.9039
q = 1-0.9039 = 0.0961
Mean = np
np = 16 * 0.9039 = 14.4624
=

By continuity,
P(x≤15) = P(x<15.5)
At x = 15.5

Therefore
P(x≤15) = P(x<15.5) =
P(z<0.8801) =
NORMSDIST(0.8801) = 0.8106
c) Given:
X = 147
P(X>147) =

P(X>147) = P(z > 1.7391)
NORMDIST(1.7391) = 0.9590
P(X>147) = 1 - 0.9590
= 0.041