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3 years ago

8

Two kilograms of ground cinnamon is packaged into bags containing 38 g each . There will also be some cinnamon left over . How m

any bags will there be

1 answer:

Kobotan [32]3 years ago

5 0

Answer:

52

Step-by-step explanation:

2 kg is the same as 2000 g.

2000 g / 38 g = 52.6

There will be 52 bags (with some cinnamon left over).

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When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

sergiy2304 [10]

Answer:

(a) P(X=3) = 0.093

(b) P(X≤3) = 0.966

(c) P(X≥4) = 0.034

(d) P(1≤X≤3) = 0.688

(e) The probability that none of the 25 boards is defective is 0.277.

(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.

Step-by-step explanation:

We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.

Let X = <em>the number of defective boards in a random sample of size, n = 25</em>

So, X ∼ Bin(25,0.05)

The probability distribution for the binomial distribution is given by;

$P(X=r)= \binom{n}{r} \times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,......$

where, n = number of trials (samples) taken = 25

r = number of success

p = probability of success which in our question is percentage

of defectivs, i.e. 5%

(a) P(X = 3) = $\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $2300 \times 0.05^{3}\times 0.95^{22}$

= <u>0.093</u>

(b) P(X $\leq$ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= <u>0.966</u>

(c) P(X $\geq$ 4) = 1 - P(X < 4) = 1 - P(X $\leq$ 3)

= 1 - 0.966

= <u>0.034</u>

<u></u>

(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

= $\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}$

= $25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}$

= <u>0.688</u>

(e) The probability that none of the 25 boards is defective is given by = P(X = 0)

P(X = 0) = $\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}$

= $1 \times 1\times 0.95^{25}$

= <u>0.277</u>

(f) The expected value of X is given by;

E(X) = $n \times p$

= $25 \times 0.05$ = 1.25

The standard deviation of X is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{25 \times 0.05 \times (1-0.05)}$

= <u>1.089</u>

8 0

3 years ago

Sally must have at least $200 in her savings account to avoid a

xxMikexx [17]

Answer:

675$

Step-by-step explanation:

got it right

7 0

2 years ago

A newsletter publisher believes that less than 58% of their readers own a Rolls Royce. For marketing purposes, a potential adver

quester [9]

Answer:

We don´t have at 95% of confidence, evidence to reject the publisher´s claim

Step-by-step explanation:

Population mean p₀ = 58 % or p₀ = 0,58

Hypothesis Test:

Null Hypothesis H₀ p = p₀

Alternative Hypothesis Hₐ p < p₀

For a significance level α = 0,05 means that CI = 95 % or CI = 0,95

z(c) = - 1,64

MOE = z(c)* √(p*q)/n

p - p₀ / √(p*q)/n = z(s)

And that z(s) is in the acceptance region

|z(s)| < |z(c)|

|z(s)| < 1,64

Then if that so we fail to reject H₀ . We don´t have evidence to reject the publisher´s claim

8 0

3 years ago

The city planning committee is composed of 12 women and l4 menWhat fraction of the committee is composed of men?

Mazyrski [523]

to solve you must dive 14 by 12 then simplify to the nearsest tenth.

3 0

3 years ago

Read 2 more answers

Identify the number of solutions:<br> 5x + 4 = 5x + 4

Murrr4er [49]

Answer:

0,4) : not a solution

(-2,4) ; solution

(0,5) : solution

(-2,7) : solution

(-4,1) : not a solution

(-1,1) : not a solution

(-1.5,3.5) : solution

any point that falls in the grey area is a solution....if ur points lie on a dashed line, it is not a solution...but if ur points lie on a solid line, it is a solution

Step-by-step explanation:

6 0

3 years ago