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MrRissso [65]
3 years ago
13

There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow, and 2 pairs of green. You select the gloves in the da

rk and can check them only after a selection has been made. What is the smallest number of gloves you need to select to have at least one matching pair in the best case?
Engineering
1 answer:
antiseptic1488 [7]3 years ago
3 0

Answer:

Best case = 2 gloves

Given Information:

Red gloves = 5 pairs

Yellow gloves = 4 pairs

Green gloves = 2 pairs

smallest number of gloves you need to select to have at least one matching pair in the best case = ?

Explanation:

How many gloves do you need to make one matching pair?

2

Yes, you are right. 2 gloves makes a matching pair and it is the smallest number of gloves you need to select to have at least one matching pair.

But what about worst case?

lets say

you tried all 5 red gloves either all of them were left or right

then you tried 4 yellow gloves either all of them were left or right

then you tried 2 green gloves either all of them were left or right

Now all the left or right gloves are tried (5 + 4 + 2 = 11) and the 12th one will definitely be either matching red, yellow or green.

Therefore, in the worst case scenario, the smallest number of gloves you need to select to have at least one matching pair is 12.

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shutvik [7]

The number of trays that should be prepared if the owner wants a service level of at least 95% is; 7 trays

<h3>How to utilize z-score statistics?</h3>

We are given;

Mean; μ = 15

Standard Deviation; σ = 5

We are told that the distribution of demand score is a bell shaped distribution that is a normal distribution.

Formula for z-score is;

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We want to find the value of x such that the probability is 0.95;

P(X > x) = P(z > (x - 15)/5) = 0.95

⇒ 1 -  P(z ≤ (x - 15)/5) = 0.95

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P(z ≤ (x - 15)/5) = 1 - 0.95

P(z ≤ (x - 15)/5) = 0.05

The value of z from the z-table of 0.05 is -1.645

Thus;

(x - 15)/5 = -1.645

x ≈ 7

Complete Question is;

A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is normal with a mean of 15 trays and standard deviation of 5 trays. If the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? Assume doughnuts have no salvage value after the day is complete. 6 5 4 7 unable to determine with the above information.

Read more about Z-score at; brainly.com/question/25638875

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