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nirvana33 [79]
1 year ago
11

It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry a

s well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally the practice of underfilling is that which one hopes to avoid. Let P(C) = 0.052 while P(A) = 0.940. (a) What is the probability that the box is underfilled, P(B)? (b) Find P(A ∩ B). (c) Are A and B mutually exclusive events? Why or why not? (d) Find P(A ∪ B). (e) What is the probability that the machine does not overfill? (f) What is the probability that the machine either overfills or underfills?
Mathematics
1 answer:
Sphinxa [80]1 year ago
5 0

Answer:

(a) P(B) = 0.008, (b) P(A∩B) = 0, (c) Yes, A and B are mutually exclusive events, (d) P(A∪B)=0.948, (e) 0.948, (f) 0.06

Step-by-step explanation:

We have three different posibilities

A: fill to specification

B: underfill

C: overfill

in probability the sum of the different events which are mutually exclusive should sum to 1, so, we should have

(a) P(B) = 1 - P(A)-P(C) = 1-0.940-0.052=0.008

(b) P(A∩B)=probability that the machine fill to specification and underfill = 0 because a machine can't fill to specification and underfill at the same time

(c) Yes, A and B are mutually exclusive events, because a machine can't fill to specification and underfill at the same time

(d) Because A and B are mutually exclusive events we should have that

P(A∪B)=P(A)+P(B)=0.940+0.008=0.948

(e) The probability that the machine does not overfill is the same that the probability that the machine fill to specification plus the probability that the machine underfill, i.e, the probability that the machine does not overfill is P(A)+P(B)=0.948, because does not overfill is equivalent either to fill to specification or to underfill.

(f) The probability that the machine either overfill or underfills is

P(C∪B)=P(C)+P(B)=0.052+0.008=0.06 because C and B are mutually exclusive events.

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Savatey [412]
I don’t think so it’s right question
6 0
1 year ago
If 153=2(z+z)n153=2(z+z)n153, equals, 2, left parenthesis, z, plus, z, right parenthesis, n, then what is the value of 2n(2z)-19
Nostrana [21]
What you must do for this case is to rewrite the first expression to find its value.
 We have then:
 153 = 2 (z + z) n
 Rewriting:
 153 = 2n2z
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 153-193 = -40
 Answer:
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8 0
2 years ago
Grace has 1.35 pounds of strawberries, 1.4 pounds of bananas, and some apples. She has more pounds of apples than pounds of stra
satela [25.4K]

Answer:

Grace could have 1.36 pounds, 1.37 pounds, 1.38 pounds or 1.39 pounds of apples.

Step-by-step explanation:

Let a represent pounds of apples.

We have been given that Grace has 1.35 pounds of strawberries. She has more pounds of apples than pounds of strawberries.

This means that a is greater than 1.35. We can represent this information in an inequality as:

a>1.35

We are also told that Grace has 1.4 pounds of bananas. She has fewer pounds of apples than pounds of bananas. This means that a is less than 1.4. We can represent this information in an inequality as:

a

Upon combining both inequalities, we will get:

1.35

Therefore, Grace could have 1.36 pounds, 1.37 pounds, 1.38 pounds or 1.39 pounds of apples.

6 0
2 years ago
A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The
Oksanka [162]

Answer:

a) [-0.134,0.034]

b) We are uncertain

c) It will change significantly

Step-by-step explanation:

a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.

Since we assume that the variances are equal, we use the pooled variance given as

s_p^2 = \frac{ (n_1 -1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2},

where n_1 = 40, n_2 = 30, s_1 = 0.16, s_2 = 0.19.

The mean difference \mu_1 - \mu_2 = 10.85 - 10.90 = -0.05.

The confidence interval is

(\mu_1 - \mu_2) \pm t_{n_1+n_2-2,\alpha/2} \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}} = (-0.05) \pm t_{68,0.025} \sqrt{\frac{0.03}{40} + \frac{0.03}{30}}

= -0.05\pm 1.995 \times 0.042 = -0.05 \pm 0.084 = [-0.134,0.034]

b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.

c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.

6 0
2 years ago
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Aleksandr-060686 [28]

Answer: The quantity demanded is decreased by 20%.

Step-by-step explanation:

Since we have given that

Price elasticity of demand = 2

Percentage change in price  = (+)10%

We need to find the percentage change in quantity demanded.

As we know the formula:

e_D=\dfrac{\text{\% change in quantity demanded}}{\text{\% change in price}}\\\\2=\dfrac{x}{10}\\\\x=20\%

As we know that there is inverse relationship between the price and quantity demanded.

Hence, the quantity demanded is decreased by 20%.

5 0
2 years ago
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