For this case we have the following number written in scientific notation:
We know that this number is greater than zero because it is a positive number.
Therefore, the following statements are true:
p ∈ (-∞, ∞)
n must be between 1 and 10
n ∈ [1, 10]
Answer:
The following statements are correct about the number written in scientific notation:
p ∈ (-∞, ∞)
n ∈ [1, 10]
The question is incomplete. The complete question is :
In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 99th percentile? (b) What height represents the first quartile? (Round to two decimal places as needed)
Solution :
Let the random variable X represents the height of women in a country.
Given :
X is normal with mean, μ = inches and the standard deviation, σ =
inches
Let,
, then Z is a standard normal
a). Let the percentile is = a
The point a is such that,
From standard table, we get :
∴
= 6.536903 + 62.9
= 69.436903
= 69.5 (rounding off)
Therefore, the height represents the percentile = 69.5 inches.
b). Let b = height represents the first quartile.
It is given by :
From the standard normal table,
∴
= 1.895345 + 62.9
= 64.795345
= 64.8 (rounding off)
Therefore, the height represents the 1st quartile is 64.8 inches.