In a shipment of 850 widgets, 32 are found to be defective. At this rate, how many defective widgets could be expected in 22,000
1 answer:
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The 5 is represented as 50. The number is in the tens place, and 5 in the tens place means 50.
Answer:
(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.
(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Step-by-step explanation:
Let <em>X</em> = number of heads.
The probability that a head occurs in a toss of a coin is, <em>p</em> = 0.50.
The coin was tossed <em>n</em> = 100 times.
A random toss's result is independent of the other tosses.
The random variable <em>X</em> follows a Binomial distribution with parameters n = 100 and <em>p</em> = 0.50.
But the sample selected is too large and the probability of success is 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of <em> </em>(sample proportion of <em>X</em>) if the following conditions are satisfied:
- np ≥ 10
- n(1 - p) ≥ 10
Check the conditions as follows:
Thus, a Normal approximation to binomial can be applied.
So,
(a)
Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:
Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.
(b)
Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:
Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Answer:
1.5 mph
Step-by-step explanation:
The speed in the still water = 6.5 mph.
The speed of the current = x mph.
1. Two friends traveled with current for 3 hours. The speed with the current is 6.5 + x mph, so they traveled miles.
2. Two friends traveled against the current for 4 hours and 48 minutes that is hours. The speed against the current is 6.5 - x mph, so they traveled
miles.
They traveled the same distance with the current and against the current, hence,
Solve this equation: