A local newspaper claims that 90% of its

ntsibengshete81

ntsibengshete81

Answered question

2022-08-25

A local newspaper claims that 90% of its online readers are under the age

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-29Added 106 answers

To solve this problem, we will use the sample proportion and the population proportion to calculate the probability.
Let p be the population proportion of online readers under the age of 45 years, which is claimed to be 90%. Therefore, p = 0.9.
We are given a sample of 300 online readers, where 240 are under the age of 45 years. The sample proportion, denoted as p-hat (p̂), is calculated by dividing the number of readers under the age of 45 (240) by the sample size (300). Therefore, p̂ = 240/300 = 0.8.
To find the probability that the sample proportion is more than 85%, we need to calculate the z-score and use the standard normal distribution.
The formula for calculating the z-score for a sample proportion is:
z=p̂pp(1p)n
Substituting the values, we have:
z=0.80.90.9(10.9)300
Calculating this expression:
z=0.10.9(0.1)300
z=0.10.09300
z=0.10.0003
z=0.10.0173205
z5.7735
Now, we need to find the probability that the z-score is greater than -5.7735. This can be calculated using a standard normal distribution table or a calculator.
P(Z>5.7735) is almost equal to 1.
Therefore, the probability that the sample proportion of the online readers under the age of 45 years is more than 85% is approximately 1, or 100%.

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