Question

WESLUIT ma recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where represents the worst possible ife and represents the best possible life. The responses were normally distributed, with a mean of 6.2 and a standard deviation of 19. Answer parts(a)- below (a) Find the probability that a randomly selected study participant's response was less than 4 The probability that a randomly selected study participant's response was less than 4 is 0.1230 (Round to four decimal places as needed) (b) Find the probability that a randomly selected study participant's response was between 4 and 6. The probability that a randomly selected study participant's response was between 4 and 6 is (Round to four decimal places as needed) Answer Enter your answer in the answer parts reaning

Answer 1

Solution :

Given that ,

mean = $\mu$ = 6.2

standard deviation = $\sigma$ = 1.9

P(4 < x < 6) = P[(4 - 6.2)/ 1.9) < (x - $\mu$ ) /$\sigma$  < (6 - 6.2) / 1.9) ]

= P(-1.16 < z < -0.11)

= P(z < -0.11) - P(z < -1.16)

Using z table,

= 0.4562 - 0.1230

= 0.3332