These Are Less Than(<) and Greater Than(>) Symbols!!
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Solution :
Given data :
The mean length of the steel rod = 29 centimeter (cm)
The standard deviation of a normally distributed lengths of rods = 0.07 centimeter (cm)
a). We are required to find the proportion of rod that have a length of less than 28.9 centimeter (cm).
Therefore, P(x < 28.9) = P(z < (28.9-29) / 0.07)
= P(z < -1.42)
= 0.0778
b). Any rods which is shorter than 
cm or longer than 
cm that re discarded.
Therefore,
P (x < 24.84 or 25.16 < x) = P( -59.42 < z or -54.85)
= 1.052
Answer:
Step-by-step explanation:
Given that sample size is 130 >30. Also by central limit theorem, we know that mean (here proportion) of all means of different samples would tend to become normal with mean = average of all means(here proportions)
Hence we can assume normality assumptions here.
Proportion sample given = 92/130 = 0.7077
The mean proportion of different samples for large sample size will follow normal with mean = sample proportion and std error = square root of p(1-p)/n
Hence mean proportion p= 0.7077
q = 1-p =0.2923
Std error = 0.0399
For 95% confidence interval we find that z critical for 95% two tailed is 1,.96
Hence margin of error = + or - 1.96(std error)
= 0.0782
Confidence interval = (p-margin of error, p+margin of error)
= (0.7077-0.0782,0.7077+0.0782)
=(0.6295, 0.7859)
We are 95% confident that average of sample proportions of different samples would lie within these values in the interval for large sample sizes.
Answer:
8 < X < 12
Step-by-step explanation:
12 is the measure of the longest side & 8 is the measure of the smallest side. So just arrange it in ascending order.
The answer is (2x + 1)(x - 3)
