The glucose concentration of adults from Municipal X is normally distributed with mean of 75 mg/dL and standard deviation of 18 mg/dL. What is the proportion of the 30 households from Barangay Y with glucose concentration more than 105 mg/dL?
Identify what is given: μ = _ σ = _ x = _
Using the same data from number 1, construct a 90% confidence interval for x.
Identify what is given:
n = __ σ = __ x = __ z-deviate = __
LL = __
UL = __
105 is 30 above the mean ... or 30/18 standard deviations
this is a z-score of 5/3 , or 1.667
use a z-score table to find the portion of the population above this score
how about the second one?
n = 30 σ = 18 x = 75 z-deviate = 1.6
LL = 69.5
UL = 80.4
To find the proportion of households with glucose concentration more than 105 mg/dL, we need to calculate the z-score and use the z-table to find the corresponding proportion.
Given:
Mean (μ) = 75 mg/dL
Standard Deviation (σ) = 18 mg/dL
Sample Size (n) = 30
Threshold Value (x) = 105 mg/dL
To calculate the z-score, we can use the formula:
z = (x - μ) / (σ / √n)
Plugging in the values:
z = (105 - 75) / (18 / √30) = 3.34
Now, we can use the z-table to find the proportion associated with a z-score of 3.34. Looking up the z-score in the table, we find that the proportion is approximately 0.999.
Therefore, the proportion of households with glucose concentration more than 105 mg/dL is approximately 0.999, or 99.9%.
Now, let's move on to constructing a 90% confidence interval for x.
Given:
Sample Size (n) = 30
Standard Deviation (σ) = 18 mg/dL
Threshold Value (x) = ?
To construct a confidence interval, we need to use the formula:
CI = x ± (z * σ / √n)
First, we need to find the z-deviate for a 90% confidence interval. Looking up the z-value for a 90% confidence interval in the z-table, we find that z is approximately 1.645.
Plugging in the values:
CI = x ± (1.645 * 18 / √30)
Now, we can calculate the lower limit (LL) and upper limit (UL):
LL = x - (1.645 * 18 / √30)
UL = x + (1.645 * 18 / √30)
However, the value of x is not provided in the question. Please provide the value of x so that we can calculate the confidence interval.