How do I solve this?
1 answer:
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Answer:
The answers to the questions are;
A) P(X) where x = 12 is equal to 3.55 ×10⁻²
B) P(x) using the normal distribution is given by the probability distribution function and is equal to 3.453 ×10⁻²
C) The calculated probabilities of P(x=12) using the binomial probability formula and the probability distribution function differ by 9.7×10⁻⁴
D) The normal distribution be used to approximate this probability because a. because np(1-p) %u2265 ⇒ np(1-p) ≥ 10
E) c. the value of fi represents the expected proportion of observation less than or equal to the ith data value.
Step-by-step explanation:
To solve the question, we note that
n = 58
p = 0.3
x = 12
Here we have n·p = 17.4 and n·q = 40.6 both ≥ 5 that is the normal distribution can be used to estimate the probability
A) We are to use the binomial probability formula to find P(X)
Where x = 12, we have P(12) = ₅₈C₁₂×0.3¹²×0.7⁴⁶
= 891794789340×0.000000531441×7.49×10⁻⁸ = 3.55 ×10⁻²
B) Using the standard distribution table we have
the z score for x = 12 given as = -1.55
From the normal distribution table, we have the probability that value is below 12 = .06057 while the normal probability distribution function which gives the probability of a number being 12 is given by
where:
σ = Standard deviation =
μ = Sample mean = n·p = 58×0.3 =17.4
Therefore the probability density function is
C) The probabilities differ by 3.55 ×10⁻² - 3.453 ×10⁻² = 9.7×10⁻⁴
D) The normal distribution be used to approximate this probability because n·p and n·p·(n-p) ≥ 5
E) f represents the area under the curve towards left of the ith data observed in a normally distributed population.
Therefore, the value of fi represents the expected proportion of observation less than or equal to the ith data value
To solve this problem you must apply the proccedure shown below:
1- The problem says that you are swimming each 25 yard length 3 seconds faster than your personal best and you have to calculate the change in time (which you can call ) of your personal best after 200 yards.
2- To calculate this, you must multiply 200 yards by 3 seconds and divide by 25 yards, as following:
Therefore, the answer is: 24 seconds.