Question

represents the worst possible ife and 10 represents the best possible life. The In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where responses were normally distributed, with a mean of 6.4 and a standard deviation of 1.9. Answer parts (aho below (a) Find the probably that a randomly selected study participant's response was less than 4 The probably that a randomly selected study parcon response was an Round to four decapaces as needed (b) Find the probability that a randomly selected study participant's response was between and The probability that a randomly selected study participant's response was between 4 and Round to four decima ces as needed (c) Find the probability that a randomly selected study participants response was more than The probably that a rad y selected study partic pants response was more than Round to four decimal places as needed (d) y unus events Explain your reasoning Choose the correct answer below A The event paris sal because i ssan 05 OB. The events in parts and are usual because the probabies are less than 05 C. The events parts and charental because of the procesarees than 05 Cack to select your answers

Answer 1

Given, mean, p = 6.4 Standard deviation, 5= 1.9 XNN (= 6.4, 5= 1.9) Then z= - = -6.4 follows standard Normal. 1.9 a) P(x<4) - P(xt < 4-6.4) 1.9 = P(Z <-1.2632) = 0.103259 [from standard Normal Table] 0.1033 6 The probability that a randomly selected study participants resporse was less than 4in a. 1033 b) P (4CXC6)= P(4-6.4 , x-4, 6-6-41 pohy na CMT CGT MED 2632 Lz C-0.2105) = P(Z <-0.2105)-PLZ 2-1.2632) - o. 4, 6639- 0.1032 from standard Normal task] = ~ 0.31338 0.3134 The probability that a randomly selected study participants response was between 4 and bis 0.3134

a) P(+78) = P(x-> 8-6.4) 1.9 2 Plz > 0.8421) = 1- P(Z <0.8421) = 1-0.80013 4 from Standard Normal Table] = 0.199866 ñ 0.1999 probability that that a randomly selected study participants a ron was more than 2 is 0.1999 The responne d iale observed the probabilities of above all events are than greater 0.05. So, there are no unusual events.