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Troyanec [42]
3 years ago
8

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard devia

tion of 0.292 grams. Find the probability of randomly selecting a cigarette with 0.37 grams of nicotine or less. Round your answer to four decima
Mathematics
1 answer:
olga_2 [115]3 years ago
4 0

Let <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

P(<em>X</em> ≤ 0.37) = P((<em>X</em> - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(<em>Z</em> ≤ -2)

where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform <em>X</em> to <em>Z</em> using the rule <em>Z</em> = (<em>X</em> - mean(<em>X</em>))/sd(<em>X</em>).)

Given the required precision for this probability, you should consult a calculator or appropriate <em>z</em>-score table. You would find that

P(<em>Z</em> ≤ -2) ≈ 0.0228

You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,

P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95

which means

P(<em>Z</em> ≤ -2 or <em>Z</em> ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(<em>Z</em> ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

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Answer:

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Step-by-step explanation:

To calculate the probability that a randomly-chosen child from this group likes either Chess or Swimming but not Football?

We already know the number that liked chess only which is 10, we have to solve for those that liked swimming only which is

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Integrating by parts yields

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