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Mapalad Integrated High School determined students’ Body Mass Index (BMI) at the opening of classes. It has been recorded that the average height of female students is 154.2 centimeters with a standard deviation of 9 centimeters. The researcher conducted her own study and she randomly selected 40 female students. In her study, she got an average of 156.7 centimeters. Is there a reason to believe the claims of the school? Use 5% level of significance in testing the hypothesis.



A jar contains 36 red marbles numbered 1 to 36 and 50 blue marbles numbered 1 to 50. A marble is drawn at random from the jar. Find the probability of the given event. Please enter reduced fractions.



(a) The marble is red. P(red)=





(b) The marble is odd-numbered. P(odd)=





(c) The marble is red or odd-numbered. P(red or odd) =





(d) The marble is blue or even-numbered. P(blue or even)


Use the rule of inference to obtain conclusion from the each of the set of premises





“If I play hockey, then I am sore the next day.”




“I use the whirlpool if I am sore.”




“I did not use the whirlpool.”

 A hardware manufacturer produces bolts used to assemble various machines. Assume that the diameter of bolts produced by this manufacturer has an unknown population mean 𝝁 and the standard deviation is 0.1 mm. suppose the average diameter of a simple random sample of 50 bolts is 5.11 mm. (a) Calculate the margin of error of a 95% confidence interval for 𝝁.


 A hardware manufacturer produces bolts used to assemble various machines. Assume that the diameter of bolts produced by this manufacturer has an unknown population mean 𝝁 and the standard deviation is 0.1 mm. suppose the average diameter of a simple random sample of 50 bolts is 5.11 mm. (a) Calculate the margin of error of a 95% confidence interval for 𝝁.


A school wants to know the proportion of students who choose online classes as their mode of learning with 90% confidence. The first survey showed that 75% choose online classes as their mode of learning. The school wants to be accurate within 3% of the true proportion. What is the total number of sample size?


The average weight of 25 chocolate bars selected from a normally distributed population is 200 g with a standard deviation of 10 g. Find the interval estimate using 98% confidence level.


How many 3-digit numbers can be formed from digits 1 – 5 if:

a. If repetition is allowed?

b. If repetition is not allowed?


How many possible passwords are there for the following conditions: 3


digits followed by 2 letters followed by 4 digits? (3 pts)

  1. In a population of high school students algebra scores the mean 64 and the standard deviation of 6. Find the z values that corresponds to a score x = 81
  2. A geometry score is 40. If it is given than mean is 42 and the standard deviation is 7.What is the corresponding z score
  3. The average credit card debt for public school teacher is 14975. if the debut is normally distributed with a standard deviation of 5,650 find the probabilities

a. That the teacher owes at least 6,740

b. that the teacher owes more than 19270

c. that the teacher owes between 6740 and 19270


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