Answer:
A) The width is 12 cm; the average time is 3 minutes
Step-by-step explanation:
Cross multiply.
5 × y = 3 × 20
5y = 60
5y ÷ 5 = 60 ÷ 5
y = 12
The width is 12 cm. Moving onto the time.
Cross multiply.
4 × y = 12 × 1
4y = 12
4y ÷ 4 = 12 ÷ 4
y = 3
The time is 3 minutes.
Answer:
a) 0.18% of cold sufferers experience fewer than 4 days of symptoms
b) 64.40% of cold sufferers experience symptoms for between 7 and 10 days.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a. What proportion of cold sufferers experience fewer than 4 days of symptoms?
This is the pvalue of Z when X = 4. So
has a pvalue of 0.0018.
So 0.18% of cold sufferers experience fewer than 4 days of symptoms.
b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?
This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 7. So
X = 10
has a pvalue of 0.9812.
X = 7
has a pvalue of 0.3372.
So 0.9812 - 0.3372 = 0.644 = 64.40% of cold sufferers experience symptoms for between 7 and 10 days.