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Mathematics

1 answer:

shusha [124]2 years ago

7 0

Answer:

Step-by-step explanation:

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A manufacturer of televisions subjects the equipment to a comprehensive testing process for all essential functions before the t

Scorpion4ik [409]

Answer:

The probability is $P(X \le 9) =0.9138$

Step-by-step explanation:

From the question we are told that

The probability of the television passing the test is p = 0.95

The sample size is n = 10

Generally the comprehensive testing process for all essential functions follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability that at least 9 pass the test is mathematically represented as

$P(X \le 9) = P(X = 9) + P(X = 10 )$

=> $P(X \le 9) = [^{10}C_9 * (0.95)^9 * (1- 0.95)^{10-9}]+ [^{10}C_{10} * {0.95}^{10} * (1- 0.95)^{10-10}]$

=> $P(X \le 9) = [10 * 0.6302 * 0.05 ]+ [1 *0.5987 * 1 ]$

=> $P(X \le 9) =0.9138$

8 0

2 years ago

2. Margie Spencer wants to have $100,000 in her savings account in 20 years. If her account pays 6.6% annual

WITCHER [35]

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100000\\ P=\textit{original amount deposited}\\ r=rate\to 6.6\%\to \frac{6.6}{100}\dotfill &0.066\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &20 \end{cases}$