Question

Suppose that, in the Bondi toy shop, the number of marbles sold in a day has a mean of m= 2800 and standard deviation of s= 340.

If we calculate the mean number of marbles sold per day over 100 days for many salespeople:

1. What is the standard error of the sample mean? (integer)

2. What will be the 10th percentile of this distribution of sample means? (integer)

3. What will be the 74th percentile of this distribution of sample means? (integer)

Answer 1

Solution

Given that,

mean = = 2800

standard deviation = = 340

n = 100

= = 2800

1) = / n = 340 / 100 = 34

2) Using standard normal table,

P(Z < z) = 10%

= P(Z < z ) = 0.10

= P(Z < -1.28 ) = 0.10

z = -1.28

Using z-score formula  

= z * +   

= -1.28 * 34 + 2800

= 2756.48

10 th percentile = 2756

3) Using standard normal table,

P(Z < z) = 74%

= P(Z < z ) = 0.74

= P(Z < 0.64 ) = 0.74

z = 0.64

Using z-score formula  

= z * +   

= 0.64 * 34 + 2800

= 2821.76

74 th percentile = 2822