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mash [69]
3 years ago
5

One measure of an athlete’s ability is the height of his or her vertical leap. Many professional basketball players are known fo

r their remarkable vertical leaps, which lead to amazing dunks. DJ Stephens is the current vertical-leap record holder at 46 inches. However, the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.
1. The probability that the mean vertical leap for the 36 players will be less than 26 inches is ________

2. The probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is _______
Mathematics
1 answer:
almond37 [142]3 years ago
6 0

Answer:

(1) P(\bar X < 26 inches) = 0.0436

(2) P(27.5 inches < \bar X < 28.5 inches) = 0.2812

Step-by-step explanation:

We are given that the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.

Firstly, Let \bar X = mean vertical leap for the 36 players

Assuming the data follows normal distribution; so the z score probability distribution for sample mean is given by;

            Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean vertical  leap = 28 inches

            \sigma = standard deviation = 7 inches

            n = sample of NBA player = 36

(1) Probability that the mean vertical leap for the 36 players will be less than 26 inches is given by = P(\bar X < 26 inches)

   P(\bar X < 26) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{26-28}{\frac{7}{\sqrt{36} } } ) = P(Z < -1.71) = 1 - P(Z \leq 1.71)

                                                 = 1 - 0.95637 = 0.0436

(2) <em>Now, here sample of NBA players is 26 so n = 26.</em>

Probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is given by = P(27.5 inches < \bar X < 28.5 inches) = P(\bar X < 28.5 inches) - P(\bar X \leq 27.5 inches)

    P(\bar X < 28.5) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{28.5-28}{\frac{7}{\sqrt{26} } } ) = P(Z < 0.36) = 0.64058 {using z table}                      

    P(\bar X \leq 27.5) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{27.5-28}{\frac{7}{\sqrt{26} } } ) = P(Z \leq -0.36) = 1 - P(Z < 0.36)

                                                        = 1 - 0.64058 = 0.35942

Therefore, P(27.5 inches < \bar X < 28.5 inches) = 0.64058 - 0.35942 = 0.2812

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kow [346]

Answer:

<u>Amanda can make 1.5 or 3/2 of batches of pancakes with 11/22 of a cup of milk.</u>

Step-by-step explanation:

1. Let's review the information given to us for answering the question correctly:

Amount of milk Amanda use for a batch of pancakes = 1/3 cup

2. How many batches can she make if she only has 11/22 of a cup of milk left?

Let's simplify 11/22, dividing by 11 the numerator and the denominator,

11/22 = 1/2

Now, using the Rule of Three Simple, we can calculate the answer to this question, this way:

Number of batches = (1/2 * 1)/1/3

Number of batches = 1/2 / 1/3

Number of batches = 1/2 * 3/1 (Taking the reciprocal)

Number of batches = 3/2 = 1.5

<u>Amanda can make 1.5 or 3/2 of batches of pancakes with 11/22 of a cup of milk.</u>

4 0
2 years ago
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.9degreesf and a standard deviation of 0.67
trasher [3.6K]

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 0.67

n = number of samples = 103

From the information given, the population standard deviation is unknown hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 103 - 1 = 102

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

Looking at the t distribution table,

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Confidence interval = 98.6 ± 0.173

This suggests that the mean body temperature could very possibly be

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3 0
3 years ago
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iVinArrow [24]
83-63=20
So your answer is 20
5 0
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600 thousands = how many tens?
san4es73 [151]
The answer is 60,000. because it would equal six hundred thousand, and that divided by 10 is 60,000
8 0
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