Science pls help this is due today
2 answers:
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Answer:
The two readings that are cutoff values are T=1.84 deg C and T=-1.84 deg C.
Step-by-step explanation:
Thermometers rejected by measurements above normal represent 3.3% of the total, which indicates, by normal probability distribution data, that accepted thermometers are 96.7% likely to measure less than the maximum allowable temperature.
This value (P(X>x)=0.967) corresponds to z = 1.8388. Since the mean and standard deviation values are the same as the standard normal probability distribution (mean = 0, sd = 0), the z value is equivalent to the measured value (temperature).
Given the symmetry of the probability distribution, we can affirm that the thermometers rejected by measurements below the permissible measured a temperature lower than -1.8388.
Answer:
The minimum head breadth that will fit the clientele is 4.4 inches.
The maximum head breadth that will fit the clientele is 7.8 inches.
Step-by-step explanation:
Let <em>X</em> = head breadths of men that is considered for the helmets.
The random variable <em>X</em> is normally distributed with mean, <em>μ</em> = 6.1 and standard deviation, <em>σ</em> = 1.
To compute the probability of a normal distribution we first need to convert the raw scores to <em>z</em>-scores using the formula:
It is provided that the helmets will be designed to fit all men except those with head breadths that are in the smallest 4.3% or largest 4.3%.
Compute the minimum head breadth that will fit the clientele as follows:
P (X < x) = 0.043
⇒ P (Z < z) = 0.043
The value of <em>z</em> for this probability is:
<em>z</em> = -1.717
*Use a <em>z</em>-table.
Compute the value of <em>x</em> as follows:
Thus, the minimum head breadth that will fit the clientele is 4.4 inches.
Compute the maximum head breadth that will fit the clientele as follows:
P (X > x) = 0.043
⇒ P (Z > z) = 0.043
⇒ P (Z < z) = 1 - 0.043
⇒ P (Z < z) = 0.957
The value of <em>z</em> for this probability is:
<em>z</em> = 1.717
*Use a <em>z</em>-table.
Compute the value of <em>x</em> as follows:
Thus, the maximum head breadth that will fit the clientele is 7.8 inches.