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The heights of the population of boys are normally distributed with a mean of 66 inches and a
standard deviation of 8.9 inches. If a random sample of 40 boys is drawn from this population,
the barangay captain wants to conduct a study to estimate average playing time of children ages 7 to 12 he wants to be 99% confident that the sample mean will be within 15 minutes of the true mean. If he can approximate a population standard deviation by 40 minutes and assume an approximately normal distribution, how large a sample should he get?
the aptitude test was administered to random sample of 120 shs students. the sample mean was 104.2 with standard deviation of 12. find 99%confidence interval
2. A random sample of n=25 measurements is selected from a population with mean μ = 3 and standard deviation = 1. What is the probability that
a. The sample mean is greater than or equal to 3.1?
b. The sample mean is greater to 2.8, but less than or equal to3.2?
Prove that for every positive integer ‘n’ : 1𝑋2𝑋3 + 2𝑋3𝑋4 + ⋯ + 𝑛(𝑛 + 1)(𝑛 + 2) =
𝑛(𝑛+1)(𝑛+2)(𝑛+3)
Determine the required probabilities.
Suppose you are to draw a ball from a box consisting of 2 red, 2 blue and 2 yellow balls twice.Let R be the random variable representing the number of Red. What is the probability of getting atleast 1 red?
Manny plans to save 1/14 of his salary each week. If his weekly salary is $420, find the amount he will save each week.
Solve the differential equation (x +4) dy/dx = x(y-3), given that y=4 when x= -3.
Show whether the following equation are exact and hence solve the equation.
a) 2x(ye^x² -1)dx + e^x²dy= 0
b) ( 6x⁵y³ + 4x³y⁵) dx + (2x⁶y² - 5x⁴y⁴) dy =0
A, B & C form the vertices of a triangle.
∠
CAB = 90°, ∠
ABC = 36° and AC = 8.8.
Calculate the length of AB rounded to 3 SF.
