Question

A normal population has a mean of 58 and a standard deviation of 13. You select a random sample of 25.

Round to 4 decimal places.

a.	34% of the time, the sample average will be less than what specific value?

Value

b.	34% of the time, the value of a randomly selected observation will be less than h. Find h.

h

c.	The probability that the sample average is more than k is 21%. Find k.

k

Answer 1

Given that,

mean = = 58

standard deviation = = 13

Using standard normal table,

P(Z < z) = 34%

= P(Z < z) = 0.34

= P(Z -0.41 ) = 0.34

z = -0.41 Using standard normal z table,

Using z-score formula  

x= z * +

x= -0.41*13+58

x= 52.67

b.

Given that,

mean = = 58

standard deviation = = 13

n = 25

= 58

= / n = 13 /25=2.6

Using standard normal table,

P(Z < z) = 34%

= P(Z < z) = 0.34

= P(Z -0.41 ) = 0.34

z = -0.41

   Using standard normal table,

Using z-score formula  

= z * +   

= -0.41 *2.6+58

= 56.93

c.

P(Z > z) = 21%

= 1 - P(Z < z) = 0.21

= P(Z < z ) = 1 - 0.21

= P(Z < z ) = 0.79

= P(Z < z ) = 0.79

z = 0.81

(using standard normal (Z) table )

Using z-score formula  

= z * +   

= 0.81 *2.6+58

k = = 60.11