The set encompasses 256 subsets. Step-by-step explanation: The elements in the set [a,b,c,d,e,f,h,i] total to 8. The total number of subsets is obtained using the formula
, where n signifies count of elements.
Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is defined as a symmetric "probability distribution centered around the mean, indicating that values near the mean are more common than those further away".
The Z-score measures a value's relation to the mean of a set of values, displayed in terms of how many standard deviations away it is from that mean.
According to the central limit theorem, "with a population having mean μ and standard deviation σ, if we draw sufficient random samples from this population with replacement, the means of those samples will resemble a normal distribution, regardless of the original population's shape, as long as the sample size is large enough".
Solution to the problem
In this scenario, we select a sample size of n = 100
The central limit theorem informs us that the distribution of the sample mean 
is defined by:
Thus, the mean for the sample would be:
And the standard deviation would be:
(a) The likelihood that all 5 eggs chosen are unspoiled is 0.0531. (b) The probability that 2 or fewer out of the 5 eggs are unspoiled is 0.3959. (c) The probability that more than 1 of the selected 5 eggs are unspoiled is 0.8747. Step-by-step explanation: The complete query is: A subpar carton of 18 eggs has 8 that are spoiled. An unsuspecting chef selects 5 eggs at random for his “Mega-Omelet Surprise.” Calculate the probability of receiving (a) exactly 5 unspoiled eggs, (b) 2 or fewer, and (c) more than 1 unspoiled egg. Define X = number of unspoiled eggs. In the faulty carton, 8 eggs are spoiled. The probability of selecting an unspoiled egg is independent of others. Provided that a chef randomly picks 5 eggs, the variable X follows a Binomial distribution with parameters n = 5 and p = 0.556. Success is defined as selecting an unspoiled egg. The probability mass function of X is as follows: (a) Calculate the probability of selecting all unspoiled eggs. Thus, this probability is found to be 0.0531. (b) For 2 or less unspoiled eggs, the probability is computed: P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2), resulting in a probability of 0.3959. (c) For more than 1 unspoiled egg: P (X > 1) = 1 - P (X ≤ 1), yields a final probability of 0.8747.
To identify the most sensible savings goal for Kirk and his family, follow these calculations:
a. $225 per month over 2 years equals $5400 (calculated as 225 * 2 * 12)
b. $200 per month for 3 years totals $7200 (calculated as 200 * 3 * 12)
c. $100 per month across 4 years will give $4800 (calculated as 100 * 4 * 12)
d. $75 saved monthly for 5 years amounts to $4500 (calculated as 75 * 5 * 12)
The optimal savings target would be option b, since $7200 exceeds <span>$6845.</span>
Answer:
0.0359
Step-by-step explanation:
Provided values:
Mean durations of three independent processes are 15, 30, and 20 minutes.
The associated standard deviations are 2, 1, and 1.6 minutes, respectively.
Thus,
New Mean = 15 + 30 + 25 = 65
Variance = (standard deviation)²
or
Variance = 2² + 1² + 1.6² = 7.56
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Standard deviation = √variance
or
Standard deviation = 2.75
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Z-value = 
or
Z-value = - 1.81
Consulting the Z-table, the Probability of Z ≤ -1.81 is equal to 0.0359.
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