Find the probability that at most 5 defective fuses will be found in a box of 200, if experience shows that 20% of such fuses are defective.
b) The following table gives the hours spent by 50 students in the playground in a week:
| Hours | 0 | 2 | 4 | 6 | 8 | 10 | |||||||
| No. of students | 10 | 6 | 8 | 6 | 10 | 10 | |||||||
Calculate the mean median and standard deviation of the hours required by students.
For the first part, we are asked to find the probability that at most 5 defective fuses are found in a box of 200, when 20% are defective. Here the number of defective fuses follows a Binomial distribution with parameters $n = 200$ and $p = 0.2$. So, the mean is $\mu = np = 200 \times 0.2 = 40$ and variance is $\sigma^2 = npq = 200 \times 0.2 ____ ___ ____ ___ ______ ______.
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एक साइकिल की दुकान 1990 से 2000 तक निम्नलिखित संख्या में साइकिलें बेचती है।
| वर्ष | बेची गई साइकिलों की संख्या (हजारों में) | |||
| 1990 | 3 | |||
| 1991 | 3 | |||
| 1992 | 3 | |||
| 1993 | 3 | |||
| 1994 | 6 | |||
| 1995 | 6 | |||
| 1996 | 6 | |||
| 1997 | 6 | |||
| 1998 | 9 | |||
| 1999 | 10 | |||
| 2000 | 12 | |||
A researcher measures the temperature of a solution 5 times. The observations are 25, 32, 27, 29, 30 °C . Determine an unbiased estimate of the temperature.
एक साबुन निर्माता यह निर्धारित करने का प्रयत्न करता है कि वह एक नए प्रकार के साबुन को बाजार में लाए या नहीं। वह संयुक्त राज्य अमेरिका से 300 व्यक्तियों का एक यादृच्छिक प्रतिदर्श चुनता है तथा इसी साइजों के प्रतिदर्श इंग्लैंड और फ्रांस से चुनता है। वह प्रत्येक प्रतिदर्श के प्रत्येक व्यक्ति से कहता है कि वह इस नए साबुन का प्रयोग करे और देखे कि वह इसे अन्य साबुनों की तुलना में अच्छा मानता है या नहीं। इससे प्राप्त परिणाम निम्नलिखित हैं:
| संयुक्त राज्य अमेरिका | इंग्लैंड | फ्रांस | |||||||
| नया साबुन पसंद करने वाले | 81 | 43 | 26 | ||||||
| पसंद नहीं करने वाले | 219 | 257 | 274 | ||||||
In a television appearance, an MLA from a state asks voters in that state to indicate whether the MLA should vote against or for a particular piece of legislation. The MLA office receives 4100 replies. Since voters from western part tends to be democrats while those from eastern parts tend to e communists, the MLA divides the replies on the basis of their geographical origin. 68% of the replies from the western part are against the legislation and 36% of the replies from the eastern part are against it.
(i) Did the MLA carry out a stratified sampling?
(ii) Did the MLA carry out a stratified random sampling?
(iii) How would you justify the sample design?
(iv) What improvements would you suggest?
एक अनुसंधानकर्ता एक घोल का तापमान पाँच बार मापता है। प्रेक्षण 25, 32, 27, 29, 30° क हैं। तापमान का एक अनभिनत आकल ज्ञात कीजिए।
There are two samples of 1200 and 900 people drawn from populations respectively, which have 30% and 25% of fair-haired people. Test whether the samples drawn from this population maintain difference or not. (Use = 0.05)
At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in weeks:
| Time | Sample number | |||||||||||||
| 1 | 2 | 3 | 4 | 5 | ||||||||||
| 9 a.m. | 8 | 9 | 15 | 4 | 11 | |||||||||
| 10 | 7 | 10 | 7 | 6 | 8 | |||||||||
| 11 | 11 | 12 | 10 | 9 | 10 | |||||||||
| 12 | 12 | 8 | 6 | 9 | 12 | |||||||||
| 1 p.m. | 11 | 10 | 6 | 14 | 11 | |||||||||
| 2 | 7 | 7 | 10 | 4 | 11 | |||||||||
| 3 | 10 | 7 | 4 | 10 | 10 | |||||||||
| 4 | 8 | 11 | 11 | 11 | 7 | |||||||||