Respuesta :
Answer:
a) sample mean = 2.63 inches
sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]
b) P(X < 2.61) = 0.0228
c.) P(2.62 < X < 2.64) = 0.6827
d.) Therefore 0.06 = P(2.6292 < X < 2.6307)
Step-by-step explanation:
i) the diameter of a brand of tennis balls is approximately normally distributed.
ii) mean = 2.63 inches
iii) standard deviation = 0.03 inches
iv) random sample of 9 tennis balls
v) sample mean = 2.63 inches
vi) sample standard deviation = [tex]\frac{standard \hspace{0.15cm} deviation}{\sqrt{n} } = \frac{0.03}{\sqrt{9} } = \frac{0.03}{3} = 0.01[/tex]
vii) the sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228
viii)the probability that the sample mean is between 2.62 and 2.64 inches
P(2.62 < X < 2.64) = 0.6827
ix) The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure
Therefore 0.06 = P(2.6292 < X < 2.6307)
a) The sampling distribution of the mean is 2.63 inches and sample standard deviation = 0.01
b) P(X < 2.61) = 0.0228
c) P(2.62 < X < 2.64) = 0.6827
d) 0.06 = P(2.6292 < X < 2.6307)
Let's solve this step by step:
Step 1: The diameter of a brand of tennis balls is approximately normally distributed.
Given:
Mean = 2.63 inches
Standard deviation = 0.03 inches
For random sample of 9 tennis balls
Step 2: Sample mean = 2.63 inches
Sample standard deviation = [tex]\frac{\text{standard deviation}}{\sqrt{n} } =\frac{0.03}{\sqrt{9} } =\frac{0.03}{3} =0.01[/tex]
Step 3: The sample mean is less than 2.61 inches = P(X < 2.61) = 0.0228
Step 4: The probability that the sample mean is between 2.62 and 2.64 inches = P(2.62 < X < 2.64) = 0.6827
Step 5: The probability is 6-% that the sample mean will be between what two values symmetrically distributed around the population measure
Therefore 0.06 = P(2.6292 < X < 2.6307)
Learn more:
brainly.com/question/17349827
