Question

The weight of a basketball is normally distributed with a mean of 17 oz and a standard deviation of 2 oz. Suppose 500 different basketballs are in a warehouse. About how many basketballs weigh more than 19 oz?

Answer 1

Answer: 80 is the correct answer !

Answer 2

79 balls.

Explanation:

We have been given that the weight of a basketball is normally distributed with a mean of 17 oz and a standard deviation of 2 oz.

Let us find the z-score for the weight 19 oz.

`z=(x-\mu)/(\sigma)`

`z=(19-17)/(2)`

`z=(2)/(2)`

`z=1`

Let us find P(z>1) using normal distribution table.

`P(z>1)=1-0.84134`

`P(z>1)=0.15866`

So the probability of a basketball having weight more than 19 oz is 0.15866. As there are 500 basketballs in the warehouse, so the total number of basketballs having a weight more than 19 oz will be:

`\text{Total number of balls having weight more than 19 oz}=500* 0.15866`

`\text{Total number of balls having weight more than 19 oz}=79.33\approx 79`

Therefore, 79 balls weigh more than 19 oz.