Respuesta :
a) The proportion of the students scored at least 26 points on this test is 0.02275.
b) The 71 percentile of the distribution of test scores is 24.073
What is meant by standard deviation?
A low standard deviation suggests that values are often close to the mean of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.
Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
Let the scores be X and X is normally distributed with a mean of 22 and standard deviation of 2.
μ=22
σ=2
X≈N(22,2)
a) P(X≥26)=P(((X-μ)/σ)≥(26-μ)/σ)
=1-P(Z≥2)
=1-P(Z<2)
=1-0.97725
=0.02275
b) Let a is the 71th percentile of X,
P(X≤a)=0.71
P((X-μ)/σ)≤(a-μ)/σ)=0.71
P(Z≤z)=0.71
From the standard normal table by calculating with z value, we get
a=24.073
Therefore,
a) The proportion of the students scored at least 26 points on this test is 0.02275.
b) The 71 percentile of the distribution of test scores is 24.073.
To know more about normal distribution, visit:
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