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Ira Lisetskai [31]
3 years ago
6

A widget inspector inspects 12 widgets and finds that exactly 3 are defective.Unfortunately, the widgets then get all mixed up a

nd the inspector has to find the 3defective widgets again by testing widgets one by one.(a) Find the probability that the inspector will now have to test at least 9 widgets.
Mathematics
2 answers:
WITCHER [35]3 years ago
8 0

Answer:

0.7455

Step-by-step explanation:

First, we note that there are CC_{12|3} = 220 ways of selecting the defective items.

The probability that the inspector will have to test at least 9 widgets would be 1 minus the probability that the inspector will have to test 8 or less widgets.

This is 1 - P(8 or less widgets have to be checked)

1 - \frac{C_{8|3} }{C_{12|3} }

= 1 - 56/220

= 1 - 0.2545

= 0.7455

rusak2 [61]3 years ago
6 0

Answer:

P[x\geq 9] = 0.0003971

Step-by-step explanation:

Given data:

n =  12

Defective widget probability is p = \frac{3}{12} = 0.25

q = 1 - p = 0.75

Probability of test atleast 9 widget is calculated by binomial distribution as

P[x\geq 9] = P(9) + P(10) +P(11) + P(12)

=\sum_{X =9}^{12} ^12C_x p^x q^{12-x}

= \sum_{X =9}^{12} ^12C_x (0.25)^x (0.75)^{12-x}

= \sum_{X =9}^{12} ^{12}C_9 (0.25)^9 (0.75)^{3} +\sum{x=9}{12} ^{12}C_{10} (0.25)^{10} (0.75)^{2} + \sum{x=9}{12} ^{12}C_{11} (0.25)^{11} (0.75)^{1}  +\sum{x=9}{12} ^{12}C_{12} (0.25)^{12} (0.75)^{0}

= 0.003541 + 0.000354+ 0.0000021 + 0.0000001

= 0.0003971

P[x\geq 9] = 0.0003971

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Calculate 15% of 68.50. then add it to the total bill.

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Keelah clothing store buys coats for $50 and then sells them for $80. What is the percent of markup on the price of the coat?
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4 0
3 years ago
in 2018 GRE scores were normally distributed with a mean of 303, and standard deviation of 13. Standford University Graduate sch
eduard

Answer:

The minimum score needed to be considered for admission to Stanfords graduate school is 328.48.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 303, \sigma = 13

What is the minimum score needed to be considered for admission to Stanfords graduate school?

Top 2.5%.

So X when Z has a pvalue of 1-0.025 = 0.975. So X when Z = 1.96

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

1.96 = \frac{X - 303}{13}

X - 303 = 13*1.96

X = 328.48

The minimum score needed to be considered for admission to Stanfords graduate school is 328.48.

3 0
3 years ago
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