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notka56 [123]
3 years ago
11

In the United States, the mean and standard deviation of adult men's heights are 70 inches (5 feet 10 inches) and 4 inches, resp

ectively. Suppose the American adult men's heights have a normal distribution Whe probability that a randomly chosen American man is taller than 6 feet (72 inches) is equal to:___________. (round off to fourth decimal place, use the given table)
a. 0.6853
b. 0.0062
c. 0.3085
d.0.6915
e. None of these
Mathematics
1 answer:
Artyom0805 [142]3 years ago
5 0

Answer:

P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)

And we can find this probability using the complement rule and the normal standard table:

P(z>0.5)=1-P(z

And the best solution would be:

c. 0.3085

Step-by-step explanation:

For this case we can convert all the values to inches in order to standardize the solution:

5ft * \frac{12 in}{1ft}= 60 in

6ft * \frac{12 in}{1ft}= 72 in

Let X the random variable that represent the heights of US mens, and for this case we know the distribution for X is given by:

X \sim N(70,4)  

Where \mu=70 and \sigma=4

We are interested on this probability

P(X>72)

We can use the z score formula given by:

z=\frac{x-\mu}{\sigma}

Using this formula we got:

P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)

And we can find this probability using the complement rule and the normal standard table:

P(z>0.5)=1-P(z

And the best solution would be:

c. 0.3085

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Answers:

w = 10 ft and l = 50 ft ................> second option

w = 20 ft and l = 60 ft ...............> third option

w = 50 ft and l = 40 ft ...............> fifth option

Explanation:

We are given that:

length should be at least 20 ...........> length ≥ 20

equation for perimeter is : 2l + 2w ≤ 200

We will check each option as follows:

Option 1:

w = 50 ft and l = 10 ft

This option is incorrect as the proposed length is less than 20.

Option 2:

w = 10 ft and l = 50 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(10) = 100 + 20 = 120 ≤ 200

The second condition is also satisfied.

This option is correct

Option 3:

w = 20 ft and l = 60 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(60) + 2(20) = 120 + 40 = 160 ≤ 200

The second condition is also satisfied.

This option is correct

Option 4:

w = 90 ft and l = 30 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(30) + 2(90) = 60 + 180 = 240 > 200

The second condition is not satisfied.

This option is incorrect

Option 5:

w = 50 ft and l = 40 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(40) = 100 + 80 = 180 ≤ 200

The second condition is also satisfied.

This option is correct

4 0
3 years ago
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