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Sphinxa [80]
3 years ago
9

As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket. The probabi

lity that a shopper will buy a packet of crackers after tasting the free sample is 0.200. Different shoppers can be regarded as independent trials. If X is the number among the next 100 shoppers who buy a packet of the crackers after tasting a free sample, then the probability that fewer than 30 buy a packet after tasting a free sample is approximately (Use Normal approximation to solve the problem, if its conditions are met.)
A. 0.2000
B. 0.9938
C. None of the answers are correct.
Mathematics
1 answer:
Veronika [31]3 years ago
6 0

Answer:

The probability that fewer than 30 buy a packet after tasting a free sample is approximately

B. 0.9938

Step-by-step explanation:

We have

p = 0.2

q = 1 - 0.2 = 0.8

n = 100

and we need to compute P(X<30). First we need to check if normal distribution can be used or not. If np>5 then we can use normal distribution to solve this problem.

np = 100*0.2 = 20 > 5.

So we can use the normal approximation to solve this problem.

μ = np = 20

σ = √(npq)

  = √(100)(0.2)(0.8)

σ = 4

We know that z = (X - μ)/σ, So

P(X<30) = P[(X-μ)/σ < (30 - μ)/σ]

              = P(z<(30-20)/4)

              = P(z < 10/4)

              = P (z<2.5)

Using the normal distribution probability table, we get:

P(z<2.5) = 0.9938

<u>So, the correct option is </u><u>B. 0.9938</u>

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What is the perimeter of a square abcd if a(0,0 and b(0,5?
Ghella [55]
So squares have 4 congruent sides. When you plot the points (0,0) and (0,5) the side length is 5 units. We can then take 5+5+5+5 and know the perimeter is 20 units.
4 0
2 years ago
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Does the equation y=14x show a proportional relationship between x and​ y? Explain.
pav-90 [236]
Yes, as x(y) increase when y(x) increases , they are proportional.
4 0
3 years ago
In which of the expressions below will x = 2.5? Select all that apply. A) 10x+209=5 B) 10x–12=38 C) 9x+18=45 D) 6x=15 E) 12x–4=2
Vinil7 [7]

Answer:

Step-by-step explanation:

6 0
2 years ago
In the distribution, the first quartile,median and mean are 30.8,48.5 and 42.0 respectively. If the co efficient skewness is -0.
finlep [7]

Answer:

The third quartile is 56.45

Step-by-step explanation:

The given parameters are;

The first quartile, Q₁ = 30.8

The median or second quartile, Q₂ = 48.5

The mean, \bar x = 42.0

Coefficient of skewness = -0.38

The Bowley's coefficient of skewness (SK) is given as follows;

SK = \dfrac{Q_3 + Q_1 - 2 \times Q_2}{Q_3 - Q_1}

Plugging in the values, we have;

-0.38 = \dfrac{Q_3 + 30.8 - 2 \times 48.5}{Q_3 - 30.8}

Which gives;

-0.38×(Q₃ - 30.8) = Q₃ + 30.8 - 2 × 48.5

11.704 - 0.38·Q₃ = Q₃ - 66.2

1.38·Q₃ = 11.704 + 66.2 =  77.904

Q₃ = 56.45

The third quartile = 56.45.

5 0
3 years ago
Leslie has a rectangular patio. She measures it and finds out it is 2135 feet long by 1115 feet wide. She wants to know how many
larisa86 [58]

Answer: (1) Leslie will need 2,380,525 square tiles (1 foot by 1 foot each)

(2) She will have to spend $1,785,393.75 to cover her patio.

Step-by-step explanation: Please refer to the picture attached.

The rectangular patio has been designed and as shown in the diagram has on side measuring 2135 ft and the other side measuring 1115 ft. This means, in order to cover the entire patio, she would have to cover an entire area defined as 2,135 feet into 1,115 feet. If one tile measures 1 foot long by 1 foot wide, the total number of tiles to cover the patio can simply be derived as;

Area = L x W

Where the length is 2135 and the width is 1115,

Area = 2135 x 1115

Area = 2380525

**Having in mind that one tile measures 1 ft by 1 ft, the area of each tile is given as

Area = L x W

Area = 1 x 1

Area = 1 square foot**

(1) The above calculation shows that Leslie would be using up a total of 2,380,525 square tiles to completely cover her patio.

(2) Having been told that each square foot of tile costs 75 cents ($0.75), the total amount spent to cover her patio would be calculated as follows;

Cost = Area x cost per tile

Cost = 2380525 x 0.75

Cost = 1785393.75

The total cost therefore is $1,785,393.75

7 0
3 years ago
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