Question

(1) A population has mean u = 6 and standard deviation o = 4. Find My and for samples of size n = 25. (2) A population has mean y = 17 and standard deviation o = 20. Find My and Og for samples of size n= 90. (3) A population has mean u = 193 and standard deviation o = 42. Find My and oz for samples of size n = 64 (4) A sample of size n = 5 will be drawn from a normal population with mean Jl = 60 and standard deviation O = 12. Find the probability that the sample mean, I will be between 50 and 70.

Answer 1

Solution:

1) Given

n = 25 sample size

. Population mean

6

. Population standard deviations

0= 4

To find $\mu_{\bar x}$

Hi

ui 6

Now find $\sigma_{\bar x}$

01 n

4 01 25

$\sigma_{\bar x}=\frac{4}{5}$

0 = 0.8

2) Given

n = 90 sample size

. Population mean

= 17

. Population standard deviations

0= 20

To find $\mu_{\bar x}$

Hi

Hi= 17

Now find $\sigma_{\bar x}$

01 n

20 01 /90

01 20 9.4868329

0 = 2.1081851

0 = 2.1082

3) Given

n = 64 sample size

. Population mean

H = 193

. Population standard deviations

0 = 42

To find $\mu_{\bar x}$

Hi

ui 193

Now find $\sigma_{\bar x}$

01 n

42 0 0 V 64

42 01

0 = 5.25

4) Given

n= 5 sample size

. Population mean

09

. Population standard deviations

0= 12

Hi

To find $\mu_{\bar x}$

09 n1

Now find $\sigma_{\bar x}$

01 n

01 12 V5

12 01 2.2360679

0 = 5.3665633

0 = 5.3666

No = 60,01 = 5.3666

To find

P(50 < i < 70

-li 70 - HE = PG 50 - Mi 01 0 0

50 - 60 = PG 5,3666 <N(0,1)< 70 – 60 5,3666

-10 = PG 5.3666 < Z< 10 5.3666

P(-1.8633771 < Z < 1.8633771

= P( Z < 1.86) - P( Z < -1.86)

= 0.9686 - 0.0314. From Z table

= 0.9372

P(50<ī <70) = 0.9372