Question

answer all and asap please

1) A large industry has an average hourly wage of $14 per hour with a standard deviation of $4. What is the probability that a random sample of 50 workers will have an average salary less than or equal to $13.75? 2) On the average, 20% of students at CSI are lefties. If 40 students are sam- pled at random, use the Central Limit Theorem to approximate the probability that at least 5 are lefties. (Use the continuity correction).

Answer 1

Here, X= 148 6 4 & = 50 Now the value - 2 - 13.75-14 4 150 - 0.4419 probability that a reandom sample of 50 workers will have an average salary less than or equal to 13.75 P(Z -0.4419) = = 0.5 -0.14 604415 0.33 33% x X

Неко, pe 20% = 0.2 n = 40 mean, es= np = gox0.2 = 8 ng - 40x0.8 - 32 variance = npg = 40x0.2 x 0.8 6.4. standared deviation 6 - [npa = 16.4 reepreesent a reandom variable which = 2.53 het, & PCX 7,5) are lebties

continuity wire rechtban, PCE, PCX7,5) = PCX 75-05) - P(x7,45) (272) W Zi2 4.5-8 . 1 2.53 wol - 1.38 -1.38 P(Z 7, 138) = -0.0838 = 0.9162 LOAN