Respuesta :
Answer:
d)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 16.5
x2 = upper bound = 23.5
u = mean = 20
s = standard deviation = 4
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.875
z2 = upper z score = (x2 - u) / s = 0.875
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.190786953
P(z < z2) = 0.809213047
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.618426094 [ANSWER]
The complete question is
A binomial probability distribution has p = 0.20 and n = 100.
What is the probability of 17 to 23 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)
Answer:
P(17 ≤ x ≤ 23) = 0.5467
Step-by-step explanation:
Using the normal approximation to this binomial distribution problem,
The mean = μ = (sample size) × (proportion) = np = 100 × 0.2 = 20.
The standard deviation = σ = √[np(1-p)] = √(100×0.2×0.8) = 4.
To now find the probability that there will be between 17 to 23 successes inclusive.
P(17 ≤ x ≤ 23)
We first normalize/standardize/obtain the z-scores of 17 and 23.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 17,
z = (x - μ)/σ = (17 - 20)/4 = - 0.75
For 23,
z = (x - μ)/σ = (23 - 20)/4 = 0.75
To determine the probability that there will be between 17 to 23 successes inclusive.
P(17 ≤ x ≤ 23) = P(-0.75 ≤ z ≤ 0.75)
We'll use data from the normal probability table for these probabilities
P(17 ≤ x ≤ 23) = P(-0.75 ≤ z ≤ 0.75)
= P(z ≤ 0.75) - P(z ≤ -0.75)
= 0.77337 - 0.22663 = 0.54674 = 0.5467 to 4 d.p.
Hope this Helps!!!
