8-5 day 2 Applications from statistics

NORMAL PROBABILITIES Probability Density Function (pdf) is a function f (x), where the domain is all real numbers, such that f (x)  0 for all x and The probability associated with an interval [a, b] is Ex 5) Find the probability that an old clock you found stopped between 2:00 and 5:00. pdf of clock:

NORMAL CURVE We need: Normal pdf (Gaussian Curve) For a population with mean  and standard deviation , the normal probability density function is

68% of area lies within  of  95% of area lies within 2 of  68-95-99.7 Rule Given a normal curve: 68% of area lies within  of  95% of area lies within 2 of  99.7% of area lies within 3 of  *Depending on the value of , the curve could be tall/skinny or short/fat

Ex 6) Suppose a telephone help line takes a mean of 2 minutes to answer calls. If the standard deviation is  = 0.5, then: ________ % of the calls are answered in the range of 1.5 to 2.5 minutes, and ________ % of the calls are answered in the range of 0.5 to 3.5 minutes 68 99.7

Ex 7) Suppose that frozen spinach boxes marked as “10 ounces” of spinach have a mean weight of 10.3 ounces and a standard deviation of 0.2 ounces. Assume that the weights of the spinach boxes are normally distributed. Formula: Quick Graph Sketch:   a) What percentage of all such spinach boxes can be expected to weigh between 10 and 11 ounces? fnInt

b) What percentage would we expect to weigh less than 10 ounces?    c) What is the probability that a box weighs exactly 10 ounces?

homework Pg. 429 # 3, 7, 10, 26, 30, 31, 38, 39