Respuesta :
Answer:
0.23.
Step-by-step explanation:
We have been given that the weight of people on a college campus are normally distributed with mean 185 pounds and standard deviation 20 pounds.
First of all, we will find the z-score corresponding to sample score 200 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z=[/tex] Z-score,
[tex]x=[/tex] Sample score,
[tex]\mu=[/tex] Mean,
[tex]\sigma=[/tex] Standard deviation.
[tex]z=\frac{200-185}{20}[/tex]
[tex]z=\frac{15}{20}[/tex]
[tex]z=0.75[/tex]
Now, we need to find [tex]P(z>0.75)[/tex]. Using formula [tex]P(z>a)=1-P(z<a)[/tex], we will get:
[tex]P(z>0.75)=1-P(z<0.75)[/tex]
Using normal distribution table, we will get:
[tex]P(z>0.75)=1-0.77337 [/tex]
[tex]P(z>0.75)=0.22663 [/tex]
Round to nearest hundredth:
[tex]P(z>0.75)\approx 0.23[/tex]
Therefore, the probability that a person weighs more than 200 pounds is approximately 0.23.
Answer:the probability that a person weighs more than 200 pounds is 0.23
Step-by-step explanation:
Since the weight of people on a college campus are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = weight of people on a college campus
u = mean weight
s = standard deviation
From the information given,
u = 185
s = 20
We want to find the probability that a person weighs more than 200 pounds. It is expressed as
P(x greater than 200) = P(x greater than 200) = 1 - P(x lesser than lesser than or equal to 200).
For x = 200,
z = (200 - 185)/20 = 0.75
Looking at the normal distribution table, the probability corresponding to the z score is 0.7735
P(x greater than 200) = 1 - 0.7735 = 0.23
