Question

The weight of a soccer ball is normally distributed with a mean of 21 oz and a standard deviation of 3 oz. Suppose 1000 different soccer balls are in a warehouse. About how many soccer balls weigh more than 24 oz
A. 40

B. 80

C. 160

D. 200

Answer 1

Answer:

The correct option is C.

Step-by-step explanation:

Given information: The weight of a soccer ball is normally distributed with a mean of 21 oz and a standard deviation of 3 oz. Total number of soccer balls is 1000.

We have to find the number of soccer balls having weight more than 24 oz.

Probability of the ball having weight more than 24 oz is

$P(x>24)=P(\frac{x-\mu}{\sigma}>\frac{24-21}{3})$

$P(x>24)=P(z>1)$

$P(x>24)=1-P(z\leq 1)$

$P(x>24)=1-P(z\leq 1)$                  (Using standard normal table)

$P(x>24)=1-0.8413$

$P(x>24)=0.1587$

The number of soccer balls having weight more than 24 oz is

$1000\times P(x>24)=1000\times 0.1587\Rightarrow 158.7\approx 160$

The number of soccer balls having weight more than 24 oz is about 160.

Therefore the correct option is C.

Answer 2

A weight of 24 oz is 1 standard deviation above the mean 21 oz. The empirical rule says approximately 68% of soccer balls have weights within 1 standard deviation (i.e. between 18 and 24 oz), so the remaining 32% of balls have weights below 18 oz or above 24 oz. The balls' weights are normally distributed, so the percentage of balls with weight less than 18 oz is the same as the percentages of balls with weight greater than 24 oz, which means about 16% of balls have weight greater than 24 oz. 16% of 1000 is 160.