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lana66690 [7]
3 years ago
12

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and tes

t 4848 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 30003000 aspirin tablets actually has a 55​% rate of​ defects, what is the probability that this whole shipment will be​ accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?
Mathematics
1 answer:
DerKrebs [107]3 years ago
8 0

Answer:

a) The probability that this whole shipment will be​ accepted is 30%.

b) Many of the shipments with this rate of defective aspirin tablets will be rejected.

Step-by-step explanation:

We have a shipment of 3000 aspirin tablets, with a 5% rate of defects.

We select a sample of size 48 and test for defectives.

If more than one aspirin is defective, the batch is rejected.

The amount of defective aspirin tablets X can be modeled as a binomial distribution random variable, with p=0.55 and n=48

We have to calculate the probabilities that X is equal or less than 1: P(X≤1).

P(X\leq1)=P(X=0)+P(X=1)\\\\\\P(0)=\binom{48}{0}(0.05)^0(0.95)^{48}=1*1*0.0853=0.0853\\\\\\P(1)=\binom{48}{1}(0.05)^1(0.95)^{47}=48*0.05*0.0897=0.2154\\\\\\P(X\eq1)=0.0853+0.2154=0.3007

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Lena [83]

Answer:

second one:  -4x +6

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3 0
3 years ago
If z varies directly as x and z=30 when x=8 find z when x=4
dangina [55]
Z=kx, 30=8k, so k=30/8=15/4 and z=15x/4, so when x=4, z=15.
8 0
3 years ago
For a data set of the pulse rates for a sample of adult? females, the lowest pulse rate is 39 beats per? minute, the mean of the
Zarrin [17]

Answer:

a) The difference is of 35 beats per minute.

b) So 3.07 standard deviations below the mean.

c) Z = -3.07.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean \mu = 74, standard deviation \sigma = 11.4

a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the? females?

39 - 74 = -35

The difference is of 35 beats per minute.

b. How many standard deviations is that? [the difference found in part? (a)?

|Z| when X = 39. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{39 - 74}{11.4}

Z = -3.07

|Z| = 3.07

So 3.07 standard deviations below the mean.

c. Convert the pulse rate of 39 beats per minutes to a z score.

From item b. above, Z = -3.07.

5 0
2 years ago
A rectangular window is topped with a semicircle the height of the rectangle part is 1 more than 3 times its width W meters whic
devlian [24]

Answer:

A = 3W² + W + 1/8πW²

Step-by-step explanation:

rectangular window is L x W

semicircle is 1/2 πr²

r = 1/2 W

L = 3W + 1

A = W(3W + 1) + 1/2 π(1/2W)²

A = 3W² + W + 1/8πW²

4 0
4 years ago
Read 2 more answers
Alice wants to put wall-to-wall carpeting in a small room with the floor plan shown.
AURORKA [14]
I found the complete problem. 

If Alice divides it into two trapezoids, the area formula would be: A = [(a+b) / 2] * h 
Trapezoid 1
A = [(7.5 + 15)/2 * 5
A = (22.5/2) * 5 
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Trapezoid 2
A = [(5 + 10)/2 * 7.5
A = (15/2) * 7.5
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Total area = 56.25 + 56.25 = 112.50 sq. ft.

3 0
3 years ago
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