Mathematics: When Emily commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 25 minutes and a standard deviation of 2.5 minutes. Out of the 203 days that Emily commutes to work per year, how many times would her commute be shorter than 21 minutes, to the nearest whole number?

When Emily commutes to work, the amount of time it

Ответ:

laleona01

17.10.2021

0.7125

Step-by-step explanation:

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes (with probability p) in a sequence of n independent events.

The probability of getting exactly x successes in n independent Bernoulli trials = $n_{C_{x}}(p)^x(1-p)^{n-x}$

Total number of watches in the shipment = 50

Number of defective watches = 6

Number of selected watches = 10

Let X denotes the number of defective digital watches such that the random variable X follows a binomial distribution with parameters n and p.

So,

Probability of defective watches = $\frac{X}{n}=\frac{6}{50}=0.12$

Take n = 10 and p = 0.12

Probability that the shipment will be rejected = $P(X\geq 1)=1-P(X=0)$

$=1-n_{C_{x}}(p)^x(1-p)^{n-x}\\=1-10_{C_{0}}(0.12)^0(1-0.12)^{10-0}$

Use $n_{C_{x}}=\frac{n!}{x!(n-x)!}$

So,

Probability that the shipment will be rejected = $=1-\left ( \frac{10!}{0!(10-0)!} \right )(0.88)^{10}$

$=1-(0.88)^{10}\\=1-0.2785\\=0.7125$

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