Amachine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 137 ounces and a standard deviation of 0.30 ounces. you randomly select 45 cans and carefully measure the contents. the sample mean of the cans is 136.9 ounces. does the machine need to be reset? explain your reasoning.

Step-by-step explanation:

Let X be the amount of paint dispensed by a machine used to fill gallon=sized paint cans.

X is Normal(137, 0.30)

Sample size = 45

Sample std error = 0.30/sqrt 45 =0.0447

x bar = 136.9

Create hypotheses as:

H0: sample mean = 137

Ha: sample mean not equal to 137

(Two tailed test)

Test statistic = (136.9-137)/0.0447

=-2.237

p value = 0.0257

Since p >0.01, at 99% level we accept null hypothesis

Machine need not be reset.

45

step-by-step explanation:

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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