Respuesta :
Answer:
79 basketballs.
Step-by-step 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 z-score for our sample score 19 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z[/tex] = z-score,
[tex]x[/tex] = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values we will get,
[tex]z=\frac{19-17}{2}[/tex]
[tex]z=\frac{2}{2}[/tex]
[tex]z=1[/tex]
Let us find P(z>1) using normal distribution table.
[tex]P(z>1)=1-P(z<1)[/tex]
[tex]P(z>1)=1-0.84134 [/tex]
[tex]P(z>1)=0.15866 [/tex]
Therefore, the probability that a basketball weigh more than 19 oz is 0.15866. Since there are 500 basketballs in warehouse, so let us multiply 0.15866 by 500 to find the number of basketballs having weight more than 19 oz.
[tex]\text{The number of basketballs weigh more than 19 oz}=0.15866\times 500[/tex]
[tex]\text{The number of basketballs weigh more than 19 oz}=79.33\approx 79 [/tex]
Therefore, 79 basketballs weigh more than 19 oz.
