Question

Question #3. A random sample of n = 9 is selected from a normal distribution with μ = 80 and σ=12. What is the probability that the sample mean will be between 75 and 86? Report to the thousandths

Question #4. A random sample of n= 4 is obtained from a normal distribution μ= 30,σ= 8. What is the probability the sample mean will be smaller than M = 22? Report to the thousandths

Question #5. A random sample of n = 9 is obtained from a normal distribution with μ= 40 and σ= 15. What is the probability that the sample mean will be greater than M =43? Report to the thousandths

Answer 1

Solution :

3 ) Given that,

mean = = 80

standard deviation = = 12

n = 9

=  80

₌ / n = 12 9 = 4

P (75 < < 86 )

P ( 75 - 80 / 4) < ( - /  ) < (86 - 80 / 4)

P ( - 5 / 4 < z < 6 / 4 )

P (-1.25 < z < 1.5 )

P ( z < 1.5 ) - P ( z < 1.25)

Using z table

= 0.9332 - 0.1056

= 0.8276

Probability = 0.8276

4 ) Given that,

mean = = 30

standard deviation = = 8

n = 4

= 30

₌ / n = 8 4 = 4

P(M < 22 )

P ( M - / ) < ( 22 - 30 / 4)

P ( z < - 8 / 4 )

P ( z < - 2 )

=0.0228

Probability = 0.0228

5 ) Given that,

mean = = 40

standard deviation = = 15

n = 9

=40

₌ / n = 15 9 = 5

P (M > 43 )

= 1 - P (M < 43 )

= 1 - P ( M -   / ) < ( 43 - 40 / 5)

= 1 - P ( z < 3 / 5 )

= 1 - P ( z < 0.6 )

Using z table

= 1 - 0.7257

= 0.2743

Probability =0.2743