THE AVERAGE  SENIOR HIGH SCHOOL IN QUEZON CITY

rachelle dabu

rachelle dabu

Answered question

2022-04-12

THE AVERAGE  SENIOR HIGH SCHOOL IN QUEZON CITY HAS 1000 STUDENT WITH A STANDARD DEVIATION OF 85 STUDENT.IF A RANDOM SAMPLE OF 38 SCHOOLS IS SELECTED.WHAT IS A PROBABILITY THAT THE MEAN NUMBER OF STUDENTS ENROLLED IS BETWEEN 970 TO 1020?

Answer & Explanation

user_27qwe

user_27qwe

Skilled2023-04-27Added 375 answers

We are given that the average number of students in a senior high school in Quezon City is μ=1000 and the standard deviation is σ=85. We want to find the probability that the mean number of students enrolled in a random sample of 38 schools is between 970 and 1020.
Let x¯ be the sample mean. We know that the distribution of x¯ is approximately normal with mean μx¯=μ=1000 and standard deviation σx¯=σn=853813.78 by the central limit theorem.
We want to find P(970x¯1020). Standardizing the values, we get:
z1=970100013.782.17andz2=1020100013.781.45
Using a standard normal table or calculator, we find that P(2.17Z1.45)0.8926, where Z is a standard normal variable.
Therefore, the probability that the mean number of students enrolled in a random sample of 38 schools is between 970 and 1020 is approximately 0.8926 or 89.26%.

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