A. 5 digit code with digits from 0-9 with no repetition.
Choices for 1st digit=10, and choices for successive digits are 9,8,7,6.
Probability of guessing it correctly on first try is
1/(10*9*8*7*6) = 1/30240
B. If zero is not in the combinations, then the domain of digits is 1-9, or 9 choices. Digits can repeat means every digit in the code has 9 choices.
Number of arrangements = 9^5 = 59049
Probability of guessing at first try = 1/59049
Answer:
a) P(X = 5) = 0.04397
b) The probability that X exceeds its mean by more than 1 standard deviation = P(z > 1) = 0.159
Step-by-step explanation:
a) This question can be solved using binomial distribution function formula
Using Binomial,
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of refrigerators to be examined before getting 5 refrigerators with defective compressors = 6
x = Number of successes required = 5
p = probability of success = probability of examining a refrigerator with defective compressor out of the total 12 = 5/12 = 0.4167
q = probability of failure = probability of examining a refrigerator without defective compressor out of the total 12 = 1 - (5/12) = 7/12 = 0.5833
P(X = 5) = ⁶C₅ (0.4167)⁵ (0.5833)⁶⁻⁵
P(X = 5) = ⁶C₅ (0.4167)⁵ (0.5833) = 1(0.01256)(0.5833) = 0.04397
P(X = 5) = 0.04397
b) The probability that X exceeds its mean by more than 1 standard deviation represents Z-score of z > 1
Using the normal distribution tables,
P(z > 1) = 1 - P(z ≤ 1) = 1 - 0.841 = 0.159
a = 3a + 12
- 3a - 3a
-2a = 12
-2 -2
a = -6
Answer: 5.87 feet per second
<u>Step-by-step explanation:</u>
Use the following conversions:
5280 feet = 1 mile, 1 hour = 60 minutes, 1 minute = 60 seconds
