While on your trip you get sick and eventually end up in the hospital. The doctor orders 120 mg of medicine to be given in the m
2 answers:
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Answer:
x = 14.42
Step-by-step explanation:
Answer:
Step-by-step explanation:
<u>System Of Equations </u>
We know the scale shows a false reading for the weights by a constant value. Let's call e the weight it adds or subtracts from the real weight it measures.
When the box is put on the scale, the real weight is b, but the scale shows
When the bag is weighted, the real value is g, but the scale shows
Finally, when both are measures, the real weight is b+g and the scale shows
We have formed a system of equations. It's easy to find the value of b, we just need to subtract the last two equations
Answer:
(a) the probability that an individual distance is greater than 214.80 cm is 0.1401.
(b) The probability that the mean for 15 randomly selected distances is greater than 204.00 cm is 0.2482.
(c) The normal distribution can be used because the original population has a normal distribution.
Step-by-step explanation:
We are given that the overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.6 cm.
(a) Let X = <em>the overhead reach distances of adult females</em>.
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean reach distance = 205.5 cm
= standard deviation = 8.6 cm
So, X ~ Normal()
Now, the probability that an individual distance is greater than 214.80 cm is given by = P(X > 214.80 cm)
P(X > 214.80 cm) = P( >
) = P(Z > 1.08) = 1 - P(Z
1.08)
= 1 - 0.8599 = <u>0.1401</u>
The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.
(b) Let = <em>the sample mean selected distances</em>.
The z-score probability distribution for the sample mean is given by;
Z = ~ N(0,1)
where, = population mean reach distance = 205.5 cm
= standard deviation = 8.6 cm
n = sample size = 15
Now, the probability that the mean for 15 randomly selected distances is greater than 204.00 cm is given by = P( > 204.00 cm)
P( > 204 cm) = P(
>
) = P(Z > -0.68) = 1 - P(Z
0.68)
= 1 - 0.7518 = <u>0.2482</u>
The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.7518.
(c) The normal distribution can be used in part (b), even though the sample size does not exceed 30 because the original population has a normal distribution and the sample of 15 randomly selected distances has been taken from the population itself.