Question

Weights of chocolate chip bags follow an approximately normal distribution with mean 11.16 ounces and a standard deviation of .15 ounce. Use this information to answer the next two questions:(use stat-crunch)

2. One bag of chocolate chips weighed 1.55 standard deviation above average. What proportion of bags weighs more than this bag? (4 decimal places)

3. The lightest 10% of chocolate chip bags weigh less than how many ounces? (3 decimal places)

Answer 1

Solution :

2)

Given that ,

mean = = 11.16

standard deviation = = 0.15

P(9.61 < x < 12.71) = P((9.61 - 11.16)/ 0.15) < (x - ) /  < (12.71 - 11.16) / 0.15) )

= 1-( P(-10.33 < z < 10.33) )

= 1 - ( P(z < 10.33) - P(z < -10.33))

= 1 - ( 1 - 0 )

= 1 - 1

= 0

Percentage = 0

3)

P(Z < z ) = 10%

P(Z < z ) = 0.10

P(Z < -1.282) = 0.10

z = -1.282

using z-score formula,

X = z* +

= -1.282* 0.15 + 11.16

= 10.968