Question

5.4/12.A. For classes of 113 ​students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.

b. For a class of 113 ​students, would two be an unusually high number who were born on the 4th of​ July?

5.3/17. A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 18 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3.0​% rate of​ defects, what is the probability that this whole shipment will be​ accepted?

The probability that this whole shipment will be accepted is.

​(Round to three decimal places as​ needed.)

Answer 1

5.3/12

data is misising, so i am answering next question

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5.3/17

The entire shipment is accepted if at most 2 tablets do not meet the required specifications.

tablets actually has a 3.0​% rate of​ defects

Sample size , n =    18
Probability of an event of interest, p =   0.03

it is a binomial probability distribution,      
      
and probability is given by      

P(X=x) = C(n,x)*px*(1-p)(n-x)

P ( X =    0   ) = C(   18   ,   0   )*   0.03   ^   0   *   0.97   ^   18=0.578
P ( X =    1   ) = C(   18   ,   1   )*   0.03   ^   1   *   0.97   ^   17=0.3217
P ( X =    2   ) = C(   18   ,   2   )*   0.03   ^   2   *   0.97   ^   16=0.0846

P(whole shipment will be​ accepted) = P(X≤2) = P(X=0)+P(X=1)+P(X=2)=0.5780+0.3217+0.0846 = 0.984