The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and
1 answer:
Answer:
They spend at least 69.48 minutes reading the paper.
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:
For the 10% who spend the most time reading the paper, how much time do they spend?
They spend at least X minutes, in which X is the value of X when Z has a pvalue of 0.90. So it is X when Z = 1.28.
They spend at least 69.48 minutes reading the paper.
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a. percent of pig pregnancies that are longer than 106 days
Since we have a normal distribution here and the average number of days is 106, we can say that 50% of the pig pregnancies are longer than 106 days.
b. percent of pig pregnancies that are shorter than 111 days
To get the percentage, we will have to convert x = 111 days into a z-score first. The formula is:
where x = raw data, μ = population mean, and σ = population SD.
Since these 3 pieces of information are already given in the question, let's plug them into the equation above.
Therefore, 111 days is located 1 standard deviation to the right of the mean.
To find the percentage of pig pregnancies shorter than 111 days, we need to find the area covered to the left of 1 SD.
To find the area covered to the left of 1SD, we need to use the standard normal distribution table.
Based on the table, the area covered to the left of 1SD is 0.8413. Multiplying the area by 100, we get 84.13. Therefore, 84.13% of the pig pregnancies are shorter than 111 days.
