The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 stude
2 answers:
Answer:
<em>2</em><em> students failed in the final exam.</em>
Step-by-step explanation:
The scores on a final exam were approximately normally distributed.
We know that,
X = raw score = 60
μ = mean = 82
σ = standard deviation = 11
Putting the values,
From Normal distribution table, we get
Hence, 2.27% of 85 students failed the final exam.
So the number of students who failed the exam is,
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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.