The number of marshmallows in a 24 oz. box of Lucky Charms Cereal is normally distributed...

This is a normal distribution question with

a) x = 110

P(x < 110.0)=?

The z-score at x = 110.0 is,

z = \frac{110.0-100.0}{15.0}

z = 0.6667

This implies that

P(x < 110.0) = P(z < 0.6667) = \textbf{0.7475181106016127}=0.75

b) x1 = 80

x2 = 120

P(80.0 < x < 120.0)=?

This implies that

P(80.0 < x < 120.0) = P(-1.3333 < z < 1.3333) = P(Z < 1.3333) - P(Z < -1.3333)

P(80.0 < x < 120.0) = 0.9087833131501531 - 0.09121668684984685

P(80.0 < x < 120.0) = \textbf{0.8176}=0.82

c) Given in the question

top 3% means bottom 97%

P(X < x) = 0.97

This implies that

P(Z < 1.8807936081512509) = 0.97

With the help of formula for z, we can say that

d) Given in the question

means data is separated from bottom 90%

P(X < x) = 0.1

This implies that

P(Z < -1.2815515655446004) = 0.1

With the help of formula for z, we can say that

PS: you have to refer z score table to find t