The numbers of items purchased by 150 randomly selected customers at a clothing store are shown in the table.
Clothing Store Purchases
Number of Items Number of Customers
0 25
1 20
2 60
3 40
4 or more 5
Based on this information, how many of the next 200 customers should be expected to purchase 2 or fewer items?
To find the expected number of customers purchasing 2 or fewer items out of the next 200 customers, we first need to find the probability of purchasing 0, 1, or 2 items.
For 0 items: 25/150 = 1/6
For 1 item: 20/150 = 1/7.5
For 2 items: 60/150 = 2/5
The probability of purchasing 2 or fewer items = P(0) + P(1) + P(2) = 1/6 + 1/7.5 + 2/5 = 0.34
Now, the expected number of customers purchasing 2 or fewer items out of the next 200 customers can be calculated as:
Expected number = 0.34 * 200 = 68
Therefore, the expected number of the next 200 customers who should be expected to purchase 2 or fewer items is 68.