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Nuetrik [128]
3 years ago
10

Blood pressure values are often reported to the nearest 5 mmhg (100, 105, 110, etc.). the actual blood pressure values for nine

randomly selected individuals are given below. 128.6 137.4 148.4 140.0 123.7 132.0 118.3 141.5 143.2 (a) what is the median of the reported blood pressure values?
Mathematics
1 answer:
sergeinik [125]3 years ago
4 0

Solution:

Given data: 128.6, 137.4, 148.4, 140.0, 123.7, 132.0, 118.3, 141.5, 143.2

Arrange in ascending order,

118.3, 123.7, 128.6, 132.0, 137.4, 140.0, 141.5, 143.2, 148.4

The number of entries are 9.

Median = (n + 1)th/2

= (9 + 1)th/2

= 5th

= 137.4

Hence, the median is 137.4.


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statuscvo [17]

Answer:

(a) The probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b) The probability that all of the selected consumers recognize the brand name is 0.0041.

(c) The probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d) The events of 5 customers recognizing the brand name is unusual.

Step-by-step explanation:

Let <em>X</em> = number of consumer's who recognize the brand.

The probability of the random variable <em>X</em> is, P (X) = <em>p</em> = 0.40.

A random sample of size, <em>n</em> = 6 consumers are selected.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.

The probability mass function of <em>X</em> is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...

(a)

Compute the value of P (X = 5) as follows:

P(X=5)={6\choose 5}0.40^{5}(1-0.40)^{6-5}\\=6\times0.01024\times0.60\\=0.036864\\\approx0.0369

Thus, the probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b)

Compute the value of P (X = 6) as follows:

P(X=6)={6\choose 6}0.40^{6}(1-0.40)^{6-6}\\=1\times 0.004096\times1\\=0.004096\\\approx0.0041

Thus, the probability that all of the selected consumers recognize the brand name is 0.0041.

(c)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = P (X = 5) + P (X = 6)

              = 0.0369 + 0.0041

              = 0.041

Thus, the probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d)

An event is considered unusual if the probability of its occurrence is less than 0.05.

The probability of 5 customers recognizing the brand name is 0.0369.

This probability value is less than 0.05.

Thus, the events of 5 customers recognizing the brand name is unusual.

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