Question

A simple random sample of size n=49 is obtained from a
population with μ=78 and σ=14. ​

(b) What isP (x>81)​?

​(c) What is (P x≤73​)? ​

(d) What is P( 76.8 less than x overbar less than 81.2)

Answer 1

Solution :

Given that ,

mean = = 78

standard deviation = = 14

= / n = 14 / 49 = 2

(b)

P( > 81) = 1 - P( < 81)

= 1 - P[( - ) / < (81 - 78) / 2]

= 1 - P(z < 1.5)

= 1 - 0.9332

= 0.0668

P( > 81) = 0.0668

(c)

P( < 73) = P(( - ) / (73 - 78) / 2)

= P(z -2.5)

= 0.0062

P( < 73) = 0.0062

(d)

= P[(76.8 - 78) /2 < ( - ) / < (81.2 - 78) / 2)]

= P(-0.6 < Z < 1.6)

= P(Z < 1.6) - P(Z < -0.6)

= 0.9452 - 0.2743

= 0.6709

P(76.8 < < 81.2) = 0.6709